text:
\section{Introduction}

Braneworld models of the Universe, where standard model (SM) particles are trapped in a three-space, while gravity might propagate also in the extra-space, have been the focus of attention in the current decade in the search for answers to several outstanding problems in theoretical physics and in cosmology. The Dvali-Gabadadze-Porrati (DGP) brane model \cite{dgp}, for instance, was explored in an attempt to understand the mystery underlaying the present accelerating pace of the cosmic expansion, without invoking the mysterious "dark energy". The DGP brane model modifies general relativity (GR) at large cosmological scales or, in other words, it carries infra-red (IR) modifications of GR. In this model the present speedup of the cosmic expansion is explained as an effect of the extra-dimension: at large cosmological scales gravity leaks into the extra space, resulting in a weakening of the gravitational bounds of the cosmic structure.\footnote{The DGP models have a ghost mode in the self-accelerating branch which raises serious doubts about it being a competing alternative to the dark energy \cite{k-koyama}.} Acting on the opposite end of the energy/curvature spectrum is the Randall-Sundrum (RS) model \cite{rs1,rs2}, which carries ultra-violet (UV) modifications of GR. This time, however, the motivation was to seek for an alternative explanation to the hierarchy problem (RS1 model \cite{rs1}), and to look for an alternative to the Kaluza-Klein compactification procedure (RS2 model \cite{rs2}). The model known as RS2 found important applications in cosmology \cite{deffayet}, in particular for the inflationary scenario \cite{hawkin-lindsay}. In this model a single codimension-1 brane with positive tension, is embedded in a five-dimensional anti-de Sitter (AdS) bulk spacetime, which is infinite in the direction perpendicular to the brane. As said, the standard model matter degrees of freedom are confined to the brane, while gravitation can propagate in the bulk. However, in the low-energy/IR limit, due to the curvature of the bulk, the graviton is confined to the brane, and standard (four-dimensional) GR laws are recovered. The latter result can be better understood if we invoke a cosmological application \cite{deffayet}: let us consider a homogeneous and isotropic Friedmann-Robertson-Walker (FRW) metric with flat spatial sections. The Friedmann equation on the RS2 brane then reads (we neglect the ''dark radiation'' and cosmological constant terms): $$3H^2=\rho(1+\rho/2\lambda),$$ where $\rho$ is the energy density of the matter degrees of freedom trapped in the brane, and $\lambda$ is the brane tension. The latter is fixed by the curvature scale of the bulk, which is constrained to be less than 0.1 mm by current tests of Newton's law \cite{roy-kazuya}. At very high energy density ($\rho\gg\lambda$), due to the brane effects, the above equation is fundamentally modified: $H\propto\rho$. As the cosmic expansion proceeds the energy content in the brane dilutes and, eventually, as long as $\rho\ll\lambda$, the standard GR behavior $H^2\propto\rho$ is recovered.

It is quite obvious that the latter result is highly dependent on the cosmic dynamics of the energy density $\rho$ itself. Actually, for fields whose energy density increases in the course of the cosmic expansion, the brane effects can be important at late-times/large cosmological scales also. This simple and obvious fact -- when analyzed in the light of the cosmological dynamics of fields trapped in the brane -- seems to contradict the spirit of the Randall-Sundrum brane scenario, which is usually assumed to modify gravity at high UV energy/curvature, with special impact on primordial (early) inflation scenario. Our trivial finding implies that, if the energy density of some (perhaps exotic) component of the cosmic mixture does not dilute but grows as expansion proceeds, then the corresponding RS-brane model can have implications not only for early-time cosmology, but it can have appreciable impact also on the fate of the cosmic expansion.

That is why, in the present paper we will explore the impact of RS brane effects on the cosmic dynamics, when the energy density of -- at least one of the components of -- the matter degrees of freedom trapped in the brane grows with the course of the cosmological expansion, instead of diluting itself. To this end we will explore the asymptotic properties of concrete models of very different nature, starting with a very elaborated toy model based on a non-linear electrodynamics (NLED) Lagrangian whose asymptotic structure is very rich. By investigating how the brane effects modify the asymptotic structure of the latter model, we will show that RS2 brane effects might convert what would have been future attractors in GR into saddle critical points. This result will be corroborated through the study of other examples of exotic matter trapped in the RS brane: i) a scalar phantom field, and ii) a tachyon phantom field. The physical consequences of the above curious ("trivial") finding will be discussed.

\section{NLED-based toy model}

As already mentioned, we start by exploring the dynamics of a non-linear electrodynamics (NLED)-based toy model. The four-dimensional (4D) Einstein-Hilbert action of gravity coupled to NLED is given by:

\be S=\int d^4x\sqrt{-g}\left[R+L_\gamma+L(F,G)\right],\label{nled action}\ee where $R$ is the curvature scalar, $L_\gamma$ -- the background perfect fluid's Lagrangian, and $L(F,G)$ is the gauge-invariant electromagnetic Lagrangian, which is a function of the electromagnetic invariants $F\equiv F^{\mu \nu}F_{\mu \nu }$ and $G\equiv\frac{1}{2}\epsilon_{\alpha\beta\mu\nu}F^{\alpha\beta}F_{\mu\nu}$ \cite{novellocqg}. As usual, the electromagnetic tensor is defined as: $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$. Standard (linear) Maxwell electrodynamics is given by the Lagrangian $L(F)=-F/4$. The corresponding field equations can be derived from the action by performing variations with respect to the spacetime metric $g_{\mu\nu}$, to obtain:

\be G_{\mu\nu}=T_{\mu\nu}^\gamma+T_{\mu\nu}^{EM},\label{feqs}\ee where

\bea &&T_{\mu\nu}^\gamma=(\rho_\gamma+p_\gamma) u_\mu u_\nu-p_\gamma g_{\mu\nu},\nonumber\\&&T_{\mu\nu}^{EM}=g_{\mu\nu}[L(F)-G L_G]-4F_{\mu\alpha}F_\nu^{\;\;\alpha} L_F,\nonumber\eea with $\rho_{\gamma}=\rho_{\gamma}(t)$, $p_\gamma=p_\gamma(t)$ -- the energy density and barotropic pressure of the background fluid, respectively, while $L_F\equiv dL/dF$, $L_{FF}\equiv d^2L/dF^2$, etc. Variation with respect to the components of the electromagnetic potential $A_\mu$ yields to the electromagnetic field equations.

In order to meet the requirements of homogeneous and isotropic cosmologies (as, in particular, the one associated with FRW spacetimes), the energy density and the pressure of the NLED field should be evaluated by averaging over volume. To do this, we define the volumetric spatial average of a quantity $X$ at the time $t$ by  (for details see \cite{novellocqg} and references therein): $$\overline{X}\equiv \lim_{V\rightarrow V_{0}}\frac{1}{V}\int d^3x \sqrt{-g}\;X\;,$$ where $V=\int d^3x\sqrt{-g}$ and $V_{0}$ is a sufficiently large time-dependent three-volume. Following the above averaging procedure, for the electromagnetic field to act as a source for the FRW model we need to impose that (the Latin indexes run over three-space); $\overline{E}_{i}=0$, $\overline{B}_{i}=0$, $\overline{E_{i}B_{j}}=0$, and also $3\overline{E_i E_j}=-E^2 g_{ij}$, $3\overline{B_i B_j}=-B^{2}g_{ij}$. Additionally it has to be assumed that the electric and magnetic fields, being random fields, have coherent lengths that are much shorter than the cosmological horizon scales. Under these assumptions the energy-momentum tensor of the electromagnetic (EM) field -- associated with the Lagrangian density $L=L(F,G)$ --, can be written in the form of the energy-momentum tensor for a perfect fluid: $$T_{\mu\nu}^{EM}=\left(\rho_B+p_B\right) u_{\mu}u_{\nu}-p_Bg_{\mu\nu},$$ where $\rho_B=-L+G L_G-4L_F E^2$, and $p_B=L-G L_G-4(2B^2-E^2) L_F/3$, with $E$ and $B$ being the averaged electric and magnetic fields, respectively. In what follows, to simplify the analysis, we shall consider a FRW universe filled with a ''magnetic fluid'', i. e., the electric component $E$ will be assumed vanishing. Even this simplified picture can give important physical insights. We will be focusing in the study of the asymptotic properties of a cosmological model with interesting features, namely a phase of current cosmic acceleration and the absence of an initial singularity, which was proposed in \cite{novellocqg} (see also \cite{23}) and is based upon the following Lagrangian density:

\be L=-\frac{1}{4}F+\alpha F^2+\beta F^{-1},  \label{L}\ee where $\alpha$ and $\beta$ are arbitrary (constant) parameters. As seen this Lagranagian contains both positive and negative powers of $F$. The second (quadratic) term dominates during very early epochs of the cosmic dynamics, while the Maxwell term (first term above) dominates in the radiation era. The last term in (\ref{L}) is responsible for the accelerated phase of the cosmic evolution \cite{novellocqg}. The above Lagrangian density yields a unified scenario to describe both the acceleration of the universe (for weak fields) and the avoidance of the initial singularity, as a consequence of its properties in the strong-field regime. Recalling that we are considering magnetic universes, i.e., $F=2B^2$, where $B^2$ is an averaged value of the magnetic field,\footnote{For details of the averaging procedure consult \cite{novellocqg}.} the stress-energy tensor associated with (\ref{L}) can be written in the form of an equivalent perfect fluid stress-energy tensor with energy density and parametric pressure: $\rho_B=B^2(1-8\alpha B^2-\beta B^{-4})/2$, and $p_B=B^2(1-40\alpha B^2+7\beta B^{-4})/6$, respectively.\footnote{Notice that, for large values of the NLED field, positivity of energy requires that $B<1/\sqrt{8\alpha }$, while, for small enough values of $B\ll 1$, if one considers positive $\beta>0$, then positivity of energy implies that $B>(7\beta)^{1/4}$. The existence of the lower bound, at first sight might appear problematic, however, given that the observational data constraints the parameter $\beta$ to be $\sqrt{|\beta|}\approx 4\times 10^{-28}\;g\;cm^{-3}$ \cite{23}, then the lower bound on $B$ can be admitted without going into conflicts with observations.}

In this paper we assume the background fluid to be dust cold dark matter (CDM), so that $\gamma=1$. Our goal will be to put the corresponding cosmological equations:

\begin{eqnarray} &&3H^2=\rho_{cdm}+\rho_B,\;\;2\dot H=-\rho_{cdm}-(\rho_B+p_B),\nonumber\\
&&\dot\rho_{cdm}+3H\rho_{cdm}=0,\;\;\dot\rho_B+3H(\rho_B+p_B)=0,\label{nled feqs}\end{eqnarray} in the form of an autonomous system of ordinary differential equations (ODE). For this purpose we choose the following phase space variables: $$x\equiv\frac{\rho_B}{3H^2},\;\;y\equiv\frac{16\alpha B^4}{3H^2},\;\;z\equiv\frac{4\beta}{3H^2 B^2}\;.$$ After this choice, the following autonomous system of ODE is obtained out of (\ref{nled feqs}):

\bea &&x'=(x-1)(x-y+z),\;\;y'=-y(5-x+y-z),\nonumber\\
&&z'=z(7+x-y+z).\label{asode}\eea Here, for generality of the analysis we shall consider arbitrary $\alpha\in\Re$ and $\beta\in\Re$. In what follows in this paper the tilde will denote derivative with respect to the new time-variable $\tau\equiv\ln a\;(d\tau=H dt)$, also known as the number of e-foldings. The phase space relevant to the present study is then given by the following region in $(x,y,z)$: $$\Psi_U=\{(x,y,z)|0\leq x\leq 1,\;(y,z)\in\Re^2,\;8x+2y+z\geq 0\},$$ where we have considered the fact that $B^2/6H^2=x+y/4+z/8$. In what follows we use the standard definition of the dimensionless density parameter for the component $X$: $\Omega_X\equiv\rho_X/3H^2$, while $\omega_X=p_X/\rho_X$ will denote the effective equation of state (EOS) parameter of the component $X$. Four equilibrium points of (\ref{asode}) in $\Psi_U$, are found:

\begin{enumerate}

\item Radiation-dominated phase: $$P_{rad}=(x,y,z)=(1,0,0),\;\;\Omega_B=1,\;\;\Omega_{cdm}=0\;.$$ This is a decelerating expansion solution ($q=1$), that is fueled by standard radiation with $\omega_B=1/3$. The eigenvalues of the linearization matrix corresponding to this equilibrium point are: $\lambda_1=1$, $\lambda_2=-4$, $\lambda_3=8$, so that it is a saddle in $\Psi_U$.

\item Infra-red NLED-dominated solution: $$P_{nled}^{IR}=(1,0,-8),\;\;\Omega_B=1,\;\;\Omega_{cdm}=0\;.$$ This is a late-time, super-inflationary solution ($q=-3$), where the NLED fluid mimics phantom behavior ($\omega_B=-7/3$). This solution exist only for $z<0$ (negative $\beta<0$). In this case there is no lower bound on the magnitude of the magnetic field. The eigenvalues of the linearization matrix for $P_{nled}^{IR}$ are: $\lambda_1=-8$, $\lambda_2=-7$, $\lambda_3=-12$, so that this solution corresponds to a late-time (future) attractor. Since, the NLED-magnetic field mimics phantom behavior, the late-time attractor might be associated with a cosmological singularity (most probably a big-rip type of singularity).

\item Ultra-violet NLED-dominated phase: $$P_{nled}^{UV}=(1,-4,0),\;\;\Omega_B=1,\;\;\Omega_{cdm}=0\;.$$ This solution corresponds to an early-time, super-stiff-fluid solution ($\omega_B=5/3$), which is associated with super-decelerating expansion ($q=3$). This solution exist only for $y<0$, i. e., if the constant $\alpha$ is a negative quantity ($\alpha<0$). Curiously, this case does not meet the conditions for a bounce (there is no upper bound on the magnitude of the magnetic field), and the corresponding cosmology starts with a big-bang singularity, since $B^2/H^2=0,\;B\neq 0,\;\Rightarrow\;H\rightarrow\infty$. This solution is a past attractor in $\Psi_U$, since the eigenvalues of the corresponding linearization matrix: $\lambda_1=5$, $\lambda_2=12$, $\lambda_3=4$, are all positive quantities. This means that this point is the starting point of every probe path in the phase space $\Psi_U$.

\item CDM-dominated solution: $$P_{cdm}=(0,0,0),\;\;\Omega_B=0,\;\;\Omega_{cdm}=1\;.$$ This phase of the cosmic evolution is characterized by decelerated expansion ($q=1/2$). The EOS parameter for the magnetic field is undefined in this case. The existence of this solution is necessary for the formation of the observed amount of structure. This is also a saddle equilibrium point in $\Psi_U$, since: $\lambda_1=-5$, $\lambda_2=7$, $\lambda_3=-1$.

\end{enumerate}

For positive definite $\alpha$ and $\beta$, only the radiation-dominated equilibrium point $P_{nled}$, and the CDM-dominated solution $P_{cdm}$, are found in $\Psi_U$. The above results confirm our expectation that a combination of positive and negative powers of the electromagnetic invariant $F$ in the NLED Lagrangian, can drive a very interesting cosmological scenario leading to accelerated expansion at late times. Unfortunately, early-time (primordial) inflation can not be obtained in the present model.

\subsection{NLED on the RS brane}

Now we explore the possible effect of RS2 braneworld gravity on the above picture. The corresponding (modified) FRW cosmological equations for a RS2 brane with CDM and a perfect fluid of NLED trapped in it, can be written as (here we omit the ''dark radiation'' term);

\bea &&3H^2=\rho_{tot}\left(1+\frac{\rho_{tot}}{2\lambda}\right),\;\;\rho_{tot}=\rho_{cdm}+\rho_B,\nonumber\\
&&2\dot H=-(\rho_{cdm}+\rho_B+p_B)\left(1+\frac{\rho_{tot}}{\lambda}\right),\nonumber\\
&&\dot\rho_{cdm}=-3H\rho_{cdm},\;\;\dot B=-2H B.\label{feqs''}\eea It is convenient to introduce the following phase space variables: $$x\equiv\frac{\rho_B}{3H^2},\;\;y\equiv\frac{16\alpha B^4}{3H^2},\;\;z\equiv\frac{4\beta}{3H^2 B^2},\;\;v\equiv\frac{\rho_{tot}}{3H^2}\;.$$ The variable $v$ controls the brane regime,

$$\Omega_\lambda\equiv\frac{\lambda}{3H^2}=\frac{v^2}{2(1-v)},$$ so that, for instance, the GR-limit (formal limit $\lambda\rightarrow\infty$) corresponds to $v=1$. The following autonomous system of ODE can be derived out of (\ref{feqs''}):

\bea &&x'=3(1-v)x+\left[\left(\frac{2-v}{v}\right)x-1\right](x-y+z),\nonumber\\
&&y'=y\left[-5+(1-v)+\left(\frac{2-v}{v}\right)(x-y+z)\right],\nonumber\\
&&z'=z\left[7+(1-v)+\left(\frac{2-v}{v}\right)(x-y+z)\right],\nonumber\\
&&v'=(1-v)(3v+x-y+z).\label{brane asode}\eea At $v=1$ the first three equations above coincide with the equations (\ref{asode}), which hold for GR with a NLED-magnetic field. The phase space of the model can be defined as follows:

\bea &&\Psi_U^{brane}=\{(x,y,z,v)|\;0\leq x\leq 1,\;\;(y,z)\in\Re^2,\nonumber\\&&\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;8x+2y+z\geq 0,\;0\leq v\leq 1\}.\nonumber\eea

The critical points of the autonomous system of ODE (\ref{brane asode}) in the phase space $\Psi_U^{brane}$, their physical properties and stability are discussed below. As in the general relativity case, four equilibrium points are found:

\begin{enumerate}

\item CDM-dominated solution: $$P_{cdm}=(0,0,0,1),\;\;\Omega_B=0,\;\;\Omega_{cdm}=1\;.$$ Since $q=1/2$, this solution is associated with decelerated expansion. The NLED-magnetic field EOS parameter $\omega_B$ is undefined. This is a saddle equilibrium point in $\Psi_U^{brane}$. Actually, the eigenvalues of the linearization matrix corresponding to this point are: $\lambda_1=-5$, $\lambda_2=7$, $\lambda_3=-3$, $\lambda_4=-1$.

\item Radiation-dominated solution: $$P_{rad}=(1,0,0,1),\;\;\Omega_B=1,\;\;\Omega_{cdm}=0\;.$$ It is also a decelerated-expansion solution ($q=1$) driven by standard (Maxwell) radiation ($\omega_B=1/3$). As the CDM-dominated phase, this solution also represents a saddle equilibrium point in $\Psi_U^{brane}$, since the eigenvalues of the linearization matrix are of opposite signs: $\lambda_1=8$, $\lambda_2=1$, $\lambda_{3,4}=-4$.

\item UV NLED-dominated solution: $$P_{nled}^{UV}=(1,-4,0,1),\;\;\Omega_B=1,\;\;\Omega_{cdm}=0\;.$$ This solution shares many properties with its similar GR-solution: it is a super-decelerated ($q=3$), super-stiff state ($\omega_B=5/3$), associated with a big-bang-type singularity ($H\rightarrow\infty$). The new feature here is that the stability properties have been modified by the brane effects. Actually, the eigenvalues of the linearization matrix in the present case are: $\lambda_1=12$, $\lambda_2=4$, $\lambda_3=5$, $\lambda_4=-8$, so that this is a saddle equilibrium point in $\Psi_U^{brane}$ (its similar GR-solution is a past attractor).

\item IR NLED-dominated solution: $$P_{nled}^{IR}=(1,0,-8,1),\;\;\Omega_B=1,\;\;\Omega_{cdm}=0\;.$$ As in the former case, this solution shares many properties with its GR-similar: it is a super-accelerated ($q=-3$), phantom-like solution ($\omega_B=-7/3$), possibly associated with a big-rip-type singularity. Other properties, the stability in particular, have been modified by the brane effects. Actually, the eigenvalues of the Jacobian matrix are $\lambda_1=-12$, $\lambda_2=-8$, $\lambda_3=-7$, $\lambda_4=4$, so that it is also a saddle equilibrium point in the phase space $\Psi_U^{brane}$.

\end{enumerate}

The first thing that is worthy of mention, is the fact that all of the critical points found represent saddle equilibrium points in the phase space $\Psi_U^{brane}$. Note that, since $v=1$, the four equilibrium points are associated with GR. In fact these coincide in almost all aspects with the ones found previously for the GR case. The first two points $P_{cdm}$, and $P_{rad}$, show no fundamental differences with their GR-similar. However, the NLED-dominated solutions $P_{nled}^{UV}$ and $P_{nled}^{IR}$, have different stability properties than their corresponding GR-solutions: while in the latter case $P_{nled}^{UV}$ was the past attractor and $P_{nled}^{IR}$ was the future attractor, in the present case both are saddle equilibrium points as already said. This means, in turn, that the space-time singularities associated with these critical points (big-bang and big-rip singularities respectively), might be evaded in the present case. Modification of the stability properties of the UV solution was expected since, as already mentioned, RS brane effects are appreciable at high energies/short distances (early times). Actually, only at very high energies can the graviton acquire large momenta along the extra dimension and may escape into the bulk (5D) spacetime. The surprise was the IR solution: it is expected that at low energies (large cosmological scales) the RS2 brane effects can be safely ignored. However, while making such statements one has to be careful. In the cosmological context, the most appreciable RS2 brane effect is to modify the Friedmann equation: $3H^2=\rho_{tot}(1+\rho_{tot}/2\lambda)$. Hence, at very high energy density $\rho_{tot}\gg\lambda$ (much bigger than the brane tension), the Friedmann equation is fundamentally modified $3H^2\propto\rho_{tot}^2$. If in the course of the cosmic expansion the total energy content of the universe dilutes, then as long as $\rho_{tot}\ll\lambda$, one recovers standard GR-Friedmann behavior. Now look at the Lagrangian density for the NLED-magnetic field (\ref{L}) considered here. Note that as the expansion proceeds the magnetic field $F\propto B^2$ dilutes, and the component $\propto\beta B^{-2}$ in (\ref{L}) grows without limit. This means that the total energy content of the universe starts growing at the expense of the NLED component so that, at late times, eventually, $\rho_{tot}$ might become much larger than the brane tension once again, rendering the brane effects important at late times also. It is then to be expected that similar IR modifications will be produced if one considers other less elaborated models such as, for instance, a scalar phantom field trapped in the RS2 braneworld.

\begin{table*}[tbp]\caption[crit]{Critical points of the autonomous system of ODE (\ref{T-ode}) for the potential $V(\phi)=V_0\phi^{-2}$ and their properties. These critical points always exist. The parameters $\lambda_1$ and $\lambda_2$ are the eigenvalues of the linearization matrices corresponding to each one of the critical points. We have defined: $y_*=\sqrt{(\lambda^2+\sqrt{\lambda^4+36})/6}$.}
\begin{tabular}{@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c}
\hline\hline\\[-0.3cm]
C. Point &$x$&$y$&$\Omega_{cdm}$ &$\Omega_\phi$& $\omega_\phi$ & $q$ & $\lambda_1$&$\lambda_2$\\[0.1cm]
\hline\\[-0.2cm]
$M$ & $0$ & $0$ & $1$ & $0$ & $-1$ & $1/2$  &$-3$&$3/2$\\[0.2cm]
$TP$&$-\lambda y_*/\sqrt{3}$&$y_*$&$0$ &$1$&$-1-\lambda^2y_*^2/3$&$-1-\lambda^2y_*^2/2$ &$-3-\lambda^2y_*^2/2$&$-3-\lambda^2y_*^2$\\[0.2cm]
\hline \hline
\end{tabular}\label{tab1}
\end{table*}

\section{The case of scalar/tachyon phantom fields}

Consider now that the source of the Einstein's field equations are a background of dark matter and a scalar phantom field $\phi$. In this case the cosmological equations coincide with (\ref{nled feqs}) but with the replacement of $\rho_B$, $p_B$ by:

\be \rho_\phi=-\frac{\dot\phi^2}{2}+V(\phi),\;\;p_\phi=-\frac{\dot\phi^2}{2}-V(\phi),\label{phantom-rho-p}\ee where $V(\phi)$ is the self-interaction potential. To write the corresponding cosmological equations in the form of an autonomous system of ODE, it suffices to choose the following phase space variables:

\be x\equiv\frac{\dot\phi}{\sqrt 6 H},\;\;y\equiv\frac{\sqrt V}{\sqrt 3 H}.\label{phantom-var}\ee The following autonomous system of ODE is obtained:

\bea &&x'=\sqrt{\frac{3}{2}}\frac{\partial_\phi V}{V} y^{2}-3x-x\frac{H'}{H},\nonumber\\
&&y'=\sqrt{\frac{3}{2}}\frac{\partial_\phi V}{V} xy-y\frac{H'}{H},\label{phantom-ode}\eea where $H'/H=-3(1-x^2-y^2)/2$. As before we can write the relevant parameters in terms of the variables $x$, $y$:

\be \Omega_\phi=y^2-x^2,\;\;\Omega_{cdm}=1+x^2-y^2,\;\;\omega_\phi=\frac{x^2+y^2}{x^2-y^2}.\nonumber\ee Notice, also, that for the deceleration parameter one has $q=-(1+H'/H)$. The phase space relevant for this case is defined by the following set: $$\Psi_{ph}=\left\{(x,y)|\;0\leq y^2-x^2\leq 1,\;\;y\geq 0\right\}.$$ For simplicity we shall consider an exponential self-interaction potential for the phantom field: $V(\phi)=V_0 \exp(-\lambda\phi)$, where $\lambda$ is a constant. For this potential the system of ODE (\ref{phantom-ode}) is closed. Only two equilibrium points are found in this case:

\begin{enumerate}

\item Matter-dominated point: $$M=(0,0),\;\;\Omega_{cdm}=1,\;\;\Omega_\phi=0,\;\;q=\frac{1}{2},$$ while the equation of state $\omega_\phi$ is undefined. The eigenvalues of the corresponding linearization (Jacobian) matrix are: $\lambda_1=-3/2$, $\lambda_2=3/2$, so that this a saddle equilibrium point.

\item Scalar phantom-dominated solution:

\bea &&SP=(-\lambda/\sqrt{6},\sqrt{1+\lambda^2/6}),\;\;\Omega_{cdm}=0,\nonumber\\
&&\Omega_\phi=1,\;\;\omega_\phi=-1-\frac{\lambda^2}{3},\;\;q=-1-\frac{\lambda^2}{2}.\nonumber\eea Notice that $\omega_\phi<-1$, $q<-1$ so that this is a supper-accelerated, phantom-dominated solution, independent of whether $\lambda$ is a positive or a negative quantity. This critical point is a future attractor in the phase space $\Psi_{ph}$ since both eigenvalues of the Jacobian matrix are negative in this case: $\lambda_1=-3-\lambda^2/2$, $\lambda_2=-3-\lambda^2$.

\end{enumerate}

Lets turn our attention now to the phantom tachyon field, for which, instead of the definition (\ref{phantom-rho-p}) for the effective energy density and pressure, one has:

\be \rho_\phi=\frac{V}{\sqrt{1+\dot{\phi}^2}}\;,\;\;p_\phi=-V\sqrt{1+\dot{\phi}^2}.\label{T-rho-p}\ee Notice that the sign of the kinetic energy under the square root has been changed. The Klein-Gordon equation for the phantom tachyon is

\be \ddot{\phi}+3H\dot{\phi}\left[1+\dot{\phi}^2\right]-\frac{\partial_\phi V}{V}\left[1+\dot{\phi}^2\right]=0.\label{klein-gordon}\ee In order to write the cosmological equations in the form of an autonomous system of ODE, in this case it is recommendable to work with the following phase space variables \cite{copeland}:

\be x\equiv\dot{\phi},\;\;y\equiv\frac{\sqrt{V}}{\sqrt{3}H}.\label{T-var}\ee Notice that, while the phase space variables (\ref{phantom-var}) were normalized by the Hubble parameter $H$, the ones in (\ref{T-var}) are not normalized (at least $x$ in (\ref{T-var}) is not a normalized variable). After the above choice, one can obtain the following autonomous system of ODE:

\bea &&x'=(x^2+1)\left[-3x+\sqrt{3}y\;\frac{\partial_\phi V}{V^{3/2}}\right]\nonumber\\
&&y'=y\left[\sqrt{\frac{3}{4}}xy\;\frac{\partial_\phi V}{V^{3/2}}-\frac{H'}{H}\right],\label{T-ode}\eea where $$\frac{H'}{H}=-\frac{3}{2}(1-y^2\sqrt{x^2+1}).$$ In terms of the variables $x$, $y$ in (\ref{T-var}), one has: $\Omega_\phi=y^2/\sqrt{1+x^2}$, while for the phantom tachyon EOS parameter, $\omega_\phi=-1-x^2$. The phase space spanned by the variables $x$ and $y$, that is relevant for an expanding Universe, can be defined as: $$\Psi_T=\{(x,y):-1\leq x\leq 1,\;0\leq y^4\leq 1-x^2\}.$$ In general the system (\ref{T-ode}) is not a closed system of ODE, unless one considers the specific case when $\lambda=\partial_\phi V/V^{3/2}$ is a constant \cite{copeland}, so that $V(\phi)=V_0 \phi^{-2}$ ($V_0=4/\lambda^2$). In what follows, for simplicity, we shall consider, precisely, the latter kind of self-interaction potential for the phantom tachyon. The critical points of (\ref{T-ode}) in this case, as well as their relevant properties, are shown in Tab. \ref{tab1}. As in the former case there are found only two critical points:

\begin{enumerate}

\item Matter-dominated solution $M=(0,0)$. This is a decelerated expansion-solution and represents a saddle point in the phase space $\Psi_T$.

\item Tachyon phantom-dominated solution $TP=(-\lambda y_*/\sqrt 3,y_*)$. In this case, since both $\omega_\phi<-1$, and $q<-1$, it is a super-accelerated, phantom solution. This equilibrium point is a future attractor in $\Psi_T$.

\end{enumerate}

The above discussed asymptotic structure is clearly illustrated in the Fig. \ref{fig1}, where the phase portraits for the scalar phantom field (left-hand panel), and for the tachyon phantom field (right-hand panel), respectively, are drawn for a given value of the brane tension ($\lambda=2$). It is apparent how the phase trajectories approach to the future attractor: the phantom-dominated solution.

\begin{figure}[t!]
\begin{center}
\includegraphics[width=6.5cm,height=6cm]{fig101.eps}\vspace{0.3cm}
\includegraphics[width=6.5cm,height=6cm]{fig102.eps}\vspace{0.3cm}
\end{center}
\caption{Phase portraits for the scalar phantom field (left-hand panel), and for the tachyon phantom field (right-hand panel), respectively. The brane tension $\lambda$ has been arbitrarily set equal to $\lambda=2$. In both cases there are no past attractors, while the phantom-dominated solution is always the future attractor.} \label{fig1}
\end{figure}

\begin{figure}[t!]
\begin{center}
\includegraphics[width=6.5cm,height=6cm]{fig201.eps}
\includegraphics[width=6.5cm,height=6cm]{fig202.eps}
\end{center}
\caption{Projections of the phase space trajectories for the scalar phantom field trapped in the RS brane, onto the phase planes $(x,z)$ and $(y,z)$, respectively. The brane tension $\lambda$ has been arbitrarily set equal to $\lambda=2$. Notice that not only the past asymptotic structure has been radically modified (there is now a past attractor: the empty Misner Universe), but also the future asymptotic has been modified: there is now no future attractor.} \label{fig2}
\end{figure}

\begin{figure}[t!]
\begin{center}
\includegraphics[width=6.5cm,height=6cm]{fig203.eps}
\includegraphics[width=6.5cm,height=6cm]{fig204.eps}
\end{center}
\caption{Projections of the phase space trajectories for the tachyon phantom field trapped in the RS brane, onto the phase planes $(x,z)$ and $(y,z)$, respectively. The brane tension $\lambda$ has been arbitrarily set equal to $\lambda=2$. The empty Universe $(0,0,0)$ is the past attractor for any probe path in the phase space, while there is no any future attractor.} \label{fig3}
\end{figure}

\begin{table*}[tbp]\caption[crit]{Critical points of the autonomous systems of ODE (\ref{phantom-brane-ode}), and (\ref{T-brane-ode}), and their properties. These critical points always exist. The parameters $\lambda_1$, $\lambda_2$, and $\lambda_3$ are the eigenvalues of the linearization matrices corresponding to each one of the critical points. The upper half of the table is for the scalar phantom field, while the lower half is for the tachyon phantom field. We have defined: $y_*=\sqrt{(\lambda^2+\sqrt{\lambda^4+36})/6}$.}
\begin{tabular}{@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c@{\hspace{14pt}}c}
\hline\hline\\[-0.3cm]
C. Point &$x$&$y$& $z$ &$\Omega_{cdm}$ &$\Omega_\phi$& $\omega_\phi$ & $q$ & $\lambda_1$&$\lambda_2$&$\lambda_3$\\[0.1cm]
\hline\\[-0.2cm]
$E$ & $0$ & $0$ & $0$ & $0$ & $0$ & undef. & $2$  &$6$& $3$ & $0$ \\[0.2cm]
$M$ & $0$ & $0$ & $1$ & $1$ & $0$ & undef. & $\frac{1}{2}$  &$-\frac{3}{2}$& $\frac{3}{2}$ & $-6$ \\[0.2cm]
$SP$&$-\frac{\lambda}{\sqrt 6}$&$\sqrt{1+\frac{\lambda^2}{6}}$ & $1$ &$0$ &$1$&$-1-\frac{\lambda^2}{3}$&$-1-\frac{\lambda^2}{2}$ &$-3-\lambda^2$&$-3-\frac{\lambda^2}{2}$ & $2\lambda^2$\\[0.2cm]
\hline \hline
$E$ & $0$ & $0$ & $0$ & $0$ & $0$ & $-1$ & $2$  &$3$& $3$ & - \\[0.2cm]
$M$ & $0$ & $0$ & $1$ & $1$ & $0$ & $-1$ & $\frac{1}{2}$  &$-3$&$\frac{3}{2}$ & $-3$ \\[0.2cm]
$TP$&$-\frac{\lambda y_*}{\sqrt 3}$ & $y_*$ & $1$ & $0$ & $1$ &$-1-\frac{\lambda^2y_*^2}{3}$&$-1-\frac{\lambda^2y_*^2}{2}$ &$-3-\frac{\lambda^2y_*^2}{2}$&$-3-\lambda^2y_*^2$ & $\lambda^2 y_*^2$ \\[0.2cm]
\hline \hline
\end{tabular}\label{tab2}
\end{table*}

\subsection{Brane effects}

Lets check now how the brane effects modify the dynamics of the scalar/tachyon phantom field. In this case we have to replace $\rho_B$ and $p_B$ in the cosmological equations (\ref{feqs''}) for matter trapped in the brane, by the corresponding expressions for the effective energy density and pressure for the scalar phantom field (\ref{phantom-rho-p}), and for the tachyon phantom field (\ref{T-rho-p}), respectively. In order to transform the corresponding field equations into an autonomous system of ODE one can use the same variables $x$, $y$ defined in (\ref{phantom-var}) for the scalar phantom field, or in (\ref{T-var}) for the tachyon phantom field, plus an additional variable:

\be z\equiv\frac{\rho_{tot}}{3H^2}.\label{z-var}\ee In terms of this variable $$\frac{\rho_{tot}}{\lambda}=\frac{2(1-z)}{z}\;\Rightarrow\;0<z\leq 1.$$ This means that general relativity is recovered at the value $z=1$. Notice that at the point $z=0$ the ratio $\rho_{tot}/\lambda$ is undefined, so that the plane set $\{(x,y,z)|\;z=0\}$ has to be removed from phase space. However, since we are interested in the asymptotic structure, we have to study, separately the limiting case $z\rightarrow 0$.

For a scalar phantom field trapped in the RS brane the autonomous system of ODE that can be obtained out of the corresponding cosmological equations is the following (compare with (\ref{phantom-ode}), $V=V_0\exp{(-\lambda\phi)}$):

\bea &&x'=-\sqrt\frac{3}{2}\lambda y^2-3x-x\frac{H'}{H},\nonumber\\
&&y'=-\sqrt\frac{3}{2}\lambda xy-y\frac{H'}{H},\nonumber\\
&&z'=6(1-z)(z-x^2-y^2),\label{phantom-brane-ode}\eea where $$\frac{H'}{H}=-\frac{3}{2}\left(\frac{2-z}{z}\right)(z-x^2-y^2).$$ As before (scalar phantom field, no brane), for the phantom field dimensionless energy density parameter, and for the EOS parameter, one has $$\Omega_\phi=y^2-x^2,\;\;\omega_\phi=\frac{x^2+y^2}{x^2-y^2}.$$ However, the expressions for the CDM dimensionless energy density parameter, and for the deceleration parameter, differ from the ones that appear after equations (\ref{phantom-ode}): $$\Omega_{cdm}=z+x^2-y^2,\;\;q=-1+\frac{3}{2}\left(\frac{2-z}{z}\right)(z-x^2-y^2).$$ The phase space relevant for this case (recall that we consider only expanding Universes so that $y\geq 0$) is given by the following set: $$\Psi_{ph}^{brane}=\{(x,y,z)|\;y^2-x^2\geq 0,\;\;y\geq 0,\;\;0<z\leq 1\}.$$

In a similar fashion, for the tachyon phantom field on the RS brane we obtain the following autonomous system of ODE (compare with (\ref{T-ode}), $V=V_0 \phi^{-2}$):

\bea &&x'=-(x^2+1)(3x-\sqrt 3\lambda y),\nonumber\\
&&y'=-y\left(-\sqrt\frac{3}{4}\lambda xy+\frac{H'}{H}\right),\nonumber\\
&&z'=3(1-z)(z-y^2\sqrt{x^2+1}),\label{T-brane-ode}\eea where $$\frac{H'}{H}=-\frac{3}{2}\left(\frac{2-z}{z}\right)(z-y^2\sqrt{x^2+1}).$$ The cosmological parameters of observational interest are given by the following expressions: $$\Omega_\phi=\frac{y^2}{\sqrt{x^2+1}},\,\;\omega_\phi=-1-x^2,\;\;\Omega_{cdm}=z-\frac{y^2}{\sqrt{x^2+1}},$$ while, as customary, for the deceleration parameter: $q=-(1+H'/H)$. The phase space where to look for the equilibrium points of (\ref{T-brane-ode}) is $$\Psi_T^{brane}=\{(x,y,z)|\;z\sqrt{x^2+1}\geq y^2,\;\;y\geq 0,\;\;0<z\leq 1\}.$$

\subsubsection{Equilibrium points and their properties}

A simple inspection of equations (\ref{phantom-brane-ode}) and (\ref{T-brane-ode}), reveals that there can be a critical point lying on the phase plane $(x,y,0)$, which has been deliberately removed from the corresponding phase spaces. Actually, the point $(0,0,0)$ seems to be a critical point of each one of the autonomous systems described in both cases. Note, however, that at this point the expression for $H'/H$ is undefined, and so are first and second equations in (\ref{phantom-brane-ode}), and second equation in (\ref{T-brane-ode}). However this fact is a consequence of the chosen phase space variables. We can apply a secure approach to study the nature of the point $(0,0,0)$. In fact, we can expand the ODEs in (\ref{phantom-brane-ode},\ref{T-brane-ode}) in the neighborhood of $(0,0,0)$: $x\rightarrow 0+\epsilon_x$, $y\rightarrow 0+\epsilon_y$, $z\rightarrow 0+\epsilon_z$, where $(\epsilon_x,\epsilon_y,\epsilon_z)$ are the small perturbations. If we retain only the linear terms in the perturbations, i. e., if neglect terms $\epsilon_x^2\sim\epsilon_y^2\sim\epsilon_z^2\sim\epsilon_x\epsilon_y\sim\epsilon_x\epsilon_z\sim\epsilon_y\epsilon_z\sim 0$, and smaller, then the autonomous systems of ODE (\ref{phantom-brane-ode}), and (\ref{T-brane-ode}), transform into the following systems of linear ODE: $$\epsilon'_x=0,\;\;\epsilon'_y=3\epsilon_y,\;\;\epsilon'_z=6\epsilon_z,$$ and $$\epsilon'_x=\sqrt{3}\lambda\epsilon_y-3\epsilon_x,\;\;\epsilon'_y=3\epsilon_y,\;\;\epsilon'_z=3\epsilon_z,$$ respectively. Hence, in the case of the scalar phantom field trapped in the RS brane, the point $(0,0,0)$ is a non-hyperbolic critical point. Most we can say in this case is that it is unstable in the directions spanned by $\partial_y$ ($\epsilon_y\propto\exp{(3\tau)}$), and $\partial_z$ ($\epsilon_z\propto\exp{(6\tau)}$). However, the phase space drawings (Fig. \ref{fig2}) reveal that it is in fact a unstable critical point, which is the past attractor in $\Psi_{ph}^{brane}$. In the case of a tachyon phantom field living in the RS brane, the point $(0,0,0)$ is also the past attractor in the phase space $\Psi_T^{brane}$. In both cases this point is associated with $\Omega_{cdm}=\Omega_\phi=0$, so that it can be identified with an empty (Misner) Universe. The point $E=(0,0,0)$ has been included in Tab. \ref{tab2}.

Here we summarize the critical points of the autonomous systems of ODE (\ref{phantom-brane-ode}) and (\ref{T-brane-ode}), and their properties (these are also displayed in Tab. \ref{tab2}):

\begin{itemize}

\item{For the scalar phantom field trapped in the brane the critical points are:}

\begin{enumerate}
\item The empty Universe solution $E=(0,0,0)$, characterized by vanishing matter content $\Omega_{cdm}=\Omega_\phi=0$, is the past attractor. This is a super-decelerating solution with $q=2$. The effective EOS parameter of the phantom field $\omega_\phi$ is undefined.
\item The matter-dominated solution $M=(0,0,1)$ ($\Omega_{cdm}=1$, $\Omega_\phi=0$) is a saddle equilibrium point in $\Psi_{ph}^{brane}$. In this case the expansion is decelerated as well ($q=1/2$).
\item The phantom-dominated solution associated with the point $SP=(-\lambda/\sqrt{6},\sqrt{1+\lambda^2/6})$ ($\Omega_\phi=1$, $\omega_\phi<-1$), is also a saddle equilibrium point in the phase space $\Psi_{ph}^{brane}$ (the third eigenvalue is a positive quantity $\lambda_3=2\lambda^2$).
\end{enumerate}

\item{For the tachyon phantom field living in the RS brane the equilibrium points are the following:}

\begin{enumerate}
\item As in the previous case the empty (Misner) Universe $E=(0,0,0)$ ($\Omega_{cdm}=\Omega_\phi=0$), associated with super-decelerated pace of the expansion ($q=2$), is the past attractor in the phase space $\Psi_T^{brane}$.
\item The matter-dominated solution $M=(0,0,1)$ ($\Omega_{cdm}=1$, $\Omega_\phi=0$) is a saddle critical point, characterized by decelerating expansion ($q=1/2$).
\item The (tachyon) phantom-dominated solution $TP=(-\lambda y_*/\sqrt{3},y_*,1)$, where we have defined $y_*=\sqrt{(\lambda^2+\sqrt{\lambda^4+36})/6}$, is also a saddle critical point in $\Psi_T^{brane}$.
\end{enumerate}

\end{itemize}

\subsection{Concluding remarks of this section}

With the study of a standard (scalar) phantom model, and of a tachyon phantom scenario, we have corroborated what we expected. The extra-dimensional brane effects modify not only the past asymptotic structure, but also the future asymptotic properties of these phantom models. Actually, by comparing the structure of the phase space of the four-dimensional (standard) models in the first part of this section, with the one emerging after considering the brane effects (former subsection), one sees that (see the figures \ref{fig1}, \ref{fig2} and \ref{fig3}):

\begin{itemize}

\item While there were no past attractors in the phase spaces $\Psi_{ph}$, $\Psi_T$ corresponding to the models (\ref{phantom-ode}), (\ref{T-ode}), respectively, for the same matter content confined to a RS2 brane, there is a past attractor: the empty Misner Universe. Hence, the brane effects modify the past asymptotic (early-times) structure of the corresponding phase spaces.

\item The matter-dominated solution is not fundamentally affected by the brane effects.

\item While the phantom-dominated solution was the future attractor in the phase spaces $\Psi_{ph}$, $\Psi_T$ corresponding to the standard (scalar) phantom model, and to the tachyon phantom model, respectively, after brane effects are considered, the stability of the above solutions is modified: the phantom-dominated solution is now a saddle critical point, so that, in the corresponding brane models there is no future attractor in the phase space.

\end{itemize}

\begin{figure}[t!]
\begin{center}
\includegraphics[width=7.5cm,height=6cm]{fig301.eps}
\end{center}
\caption{Energy density vs redshift for the toy model $\rho_{tot}(z)=\mu(z+1)^3+\sigma(1-\exp{(-\nu(z+1)^{-1})})$ (Friedmann equation (\ref{toy model})). The free parameters have been arbitrarily chosen: $\mu=0.1$, $\sigma=2$, $\nu=0.1$. The solid curve represents the evolution of the total energy density, while the darker dashed line represents the phantom energy density (the cold dark matter energy density evolution is represented by the gray dashed line).} \label{fig4}
\end{figure}

\section{Discussion and Conclusion}

Conventional wisdom convinces us that Randall-Sundrum brane scenario, which was proposed as an alternative to the Kaluza-Klein compactification procedure -- also to seek for an alternative explanation to the mass hierarchy problem --, appreciably modifies gravity only at very high energy/short scales (UV modifications only), so that it could have impact on the pace of the primordial inflation, for instance, but does not modify the late-time cosmic dynamics. However, the above statement is true only if the energy density of the matter content of the brane, dilutes with the course of the cosmic expansion, as it is true for most forms of known matter sources (radiation, dust, quintessential dark energy, etc.). What happens if those known forms of matter, are replaced by other (exotic) forms which energy density does not dilute, but increases at late times? Take, for instance, a Universe filled with a mixture of cold dark matter and of a dark energy fluid which energy density grows with the cosmic expansion according to $\rho_{ph}=\sigma(1-e^{-\nu a})$, so that the total energy density of the matter trapped in the RS brane is given by:

\be \rho_{tot}=\frac{\mu}{a^3}+\sigma(1-e^{-\nu a}).\label{toy model}\ee The behavior of the total energy density $\rho_{tot}$ vs the redshift $z$ is shown in the figure \ref{fig4}. It is seen that the cold dark matter dominates at early times and dilutes as the expansion proceeds. Meanwhile, the phantom (dark energy) density is a growing function of the redshift and, somewhere in the future starts dominating the dynamics of the expansion. The fate of the cosmic evolution ($z\rightarrow -1$) is close to a de Sitter Universe where $\rho_{tot}\approx\sigma$. Although this is an unrealistic toy model, several qualitative aspects will be well illustrated. Since the brane effects modify the Friedmann equation according to $$3H^2=\rho_{tot}\left(1+\frac{\rho_{tot}}{2\lambda}\right),$$ then, at very early times where $z\gg (2\lambda/\mu)^{1/3}$, the Friedmann equation is well approximated by $3H^2=\mu^2/2\lambda a^6$. This means that the effect of the brane at high energies and large redshifts, is to allow for a metamorphosis of the background fluid from cold dark matter into a super-relativistic stiff fluid.  At late times the modification to the standard Eisntein's dynamics is also appreciable. Actually, at late times, according to standard Friedmann equation $3H^2=\rho_{tot}\approx\sigma$, meanwhile, if brane effects are taken into consideration, then, either $3H^2\approx 3\sigma/2$ if $\sigma$ is of the same order as the brane tension ($\sigma\approx\lambda$), or $3H^2\approx\sigma^2/2\lambda$ if $\sigma\gg\lambda$. In the former case, aside from the factor $3/2$, it has to be considered, also, that $\sigma\approx\lambda$ is a very large quantity. In the latter case the energy density is boosted by the factor $\sigma/2\lambda$ which is also very large since $\sigma/\lambda\gg 1$. This shows the way brane effects might affect the cosmic dynamics not only at early times but also at late times.

While the toy model (\ref{toy model}) is a unrealistic model with no physical motivation at all, other more physically motivated models, as the scalar phantom, and tachyon phantom models, also corroborate the former results. Even in the case when the effective phantom behavior is the result of the peculiar dynamics of a cosmological fluid of known nature (the NLED-based model of section II), the extra-dimensional brane effects modify the late time dynamics. In all of these models of very different nature, the effect of the brane is to modify the stability of the solution which is associated with the future asymptotics of the models: the brane destroys the future attractor, leaving in its place a unstable saddle equilibrium point. This means that the end point of the cosmic evolution is uncertain, unlike the case when there is a future attractor which is, necessarily, the end point of the cosmological evolution. It has to be underlined that the modification of the late-time asymptotic structure by the RS brane effects occurs only for those exotic forms of matter which effective equation of state in GR is less than -1 (phantom matter).

We want to stress that the above "mixing of scales" effect, where both UV and IR modifications of general relativity are the result of a same effect (in the present case the effect of the extra-space in the Randall-Sundrum brane picture), is distinctive only of theories that modify the right-hand-side (matter part) of the Friedmann equation. In this sense, for instance, it is not to be expected that the DGP brane model -- designed to modify gravity at the IR -- can modify GR also at UV energies/curvatures. This will be the subject of a separate publication \cite{extenso}.

The authors greatly acknowledge most useful comments and criticism by the referees. This work was partly supported by CONACyT M\'{e}xico, under grants 49924-J, 105079, and Instituto Avanzado de Cosmologia (IAC) collaboration. R. G.-S. acknowledges partial support from COFAA-IPN and EDI-IPN grants, and SIP-IPN 20100610, 20110664.

redpajama_set_name: RedPajamaArXiv


text:
Compotion
Home Fatawa Fatawa of Permanent Committee Tafsir Tafsir of some Ayahs
Tafsir of Ayah 36 of Surah Al-Nur
Q 3: What is the Tafsir (explanation/exegesis) of Allah's saying (the meanings of which are translated as): In houses (mosques) which Allâh has ordered to be raised (to be cleaned, and to be honoured), in them His Name is remembered [i.e. Adhan, Iqamah, Salât (prayers), invocations, recitation of the Qur'ân etc.]. Therein glorify Him (Allah) in the mornings and in the afternoons or the evenings, ?
A: The word "houses" in this Ayah (Qur'anic verse) means Masjids (mosques) and the prepositional phrase "in houses" is related to Allah's saying in the previous Ayah: ...lit , or describe the word "lamp". Thus, the meaning is: Allah is the Light of the heavens and the earth. The likeness of His Light is as if there were a niche and within it a lamp, the lamp is in a pure crystal glass, lit by an olive oil tree in the Masjids which Allah has ordered people to build, honor, and protect from idle talk, false speech, loud voices, and all that does not befit its stature. Then, Allah (Exalted be He) orders people to mention His Name in these Masjids by heart and tongue, reciting the Adhkar (invocations and remembrances said at certain times on a regular basis) authentically reported from the Prophet (peace be upon him), unlike those who follow some Tariqahs (Sufi orders) and repeat invented forms of Dhikr (Remembrance of Allah) whose phrases and way of reciting are of their own creation. (Part No. 4; Page No. 343) In these Masjids, Muslims glorify Allah, pray, acquire religious knowledge, recite the Qur'an, and say all the Adhkar prescribed by Islam in the morning and the evening, at any time of day, whether early in the morning or late at night. Those are the Muslims who made a just estimate of Allah, such as is due to Him, so they are not diverted by worldly matters such as trade or sale from remaining mindful of Allah and remembering Him with their hearts, tongues, and the physical action of their bodies. They fear Allah (Exalted be He), keep a constant watch over the consequences of their deeds, and dread the horrors of the Day of Resurrection; the Day when hearts and eyes will fearfully turn about; when every nursing mother will forget her nursling, and every pregnant woman will drop her pregnancy, and when you shall see mankind as in a drunken state, yet they will not be drunken, but the Torment of Allah is severe. Later in the Ayahs, Allah (Exalted be He) mentions that He will reward such people according to the best of their deeds; they shall receive their reward in full, without reckoning, out of His Grace, as an appropriate recompense for their sincerity and for selling themselves only to their Lord, the Bestower of Graces, and the Owner of Great Bounty.
< 1264 Tafsir of Ayah 114 o...
< 1262 Tafsir of Ayahs 14 a...
Tafsir of Ayahs 30 and 31 of Surah Al-Naml
Tafsir of some Ayahs
Reciting Basmalah quietly in the Jahri Salah
Different opinions regarding the Tafsir of Al-Sab`-ul-Mathany
Tafsir of Ayahs 14 and 15 of Surah Al-A`la
Subscribe to our new courses
Tafsir of Ayah 114 of Surah Al-Baqarah
Tafsir of the first Ayahs of Surah Al-`Alaq
Site in digits
ba-hammam
spacechanels

redpajama_set_name: RedPajamaCommonCrawl


text:
Regulatory News - Americas
U.S. housing finance chief says Congress should create explicit guarantee for Fannie, Freddie
WASHINGTON, June 13 (Reuters) - The head of the U.S. Federal Housing Finance Agency said on Thursday that Congress should create an explicit guarantee for government-sponsored enterprises Fannie Mae and Freddie Mac.
"The explicit guarantee should be limited, clearly defined, and paid for," Mark Calabria told an audience in Washington.
"I will take whatever actions I can to fulfill these responsibilities and I will continue working closely with Congress to make the system more resilient and stable through the cycle." (Reporting by Katanga Johnson; Editing by Peter Cooney)


text: FEBRUARY 13. 1919 a a a a a a a a a a a a The British Ah- Fleet.—A view in the navigation cabin of rigid air ship "R. »." a a a a a1 a a • • a a a a a a E • a • Washington, D.C., and New York, N.Y. The wonderful success attending the operation of this new service indicates ite entire practicability, and bespeaks for it a great future. It affords a most valuable opportunity for speeding up important mail matter. On the first trip there were 3,600 pieces despatched from the Washington office. At the in stallation of the service the rate of postage, which provided far special delivery service, was 24c. (about is.) per ounce, but on July 15, 1918, this rate was reduced to 6c. frd) per ounce, with 10c. (3d.) additional fox special delivery service." LmuT.-CoL. PATJL LECLERC has been charged with the organisation of the new aeroplane service by which the devastated regions in the north of France are to be re- victualled. Several squadrons of military machines have been put at his disposal, in order that supplies—and par ticularly condensed milk for the children—may be hurried to the stricken countrv. It is estimated that something in the neighbourhood of 150 landing grounds wiH be required, outside of those already in existence, to say nothing of the signal, telephonic, meteorological and radio-telegraphic ser vices which will have to be instituted. THE BRITISH AIR FLEET The aft engine-house of one of our British rigid airships, the reversible propeller system for lifting. 2IO •* R. 39," showing


text:
The independent observer of The Global Fund
Global Fund Observer
GFO Live
OFM en direct
ОГФ в прямом эфире
GFO Newsletter
GFO Search
Contact GFO
Grant Portfolio
Global Fund Donors
Pledges and Contributions
Donor Score
Grant Performance Analysis
Glossary and Methodology
Home » Global Fund Observer » GFO Newsletter » Back Issues
Subscribe to GFO Newsletter
Issue 332 7 March 2018
1. NEWS
India plans to transition away from Global Fund support over the next nine years
India is preparing to transition away from Global Fund support –– gradually, over a nine-year period. Some transition measures have already been adopted. India's transition plans were described at some length in grant documents related to the country's 2017 funding requests for TB, HIV and malaria. We provide a summary.
Follow-up audit of Global Fund grants to Nigeria shows significant improvements, OIG says
Since the last audit in 2015, there have been significant improvements, the Office of the Inspector General says in a follow-up audit recently concluded. But there are still many problems that need to be resolved, and some of the mitigation measures already implemented need more time to become effective. The follow-up audit covered the period from July 2016 to September 2017.
Global Fund Board approves an HIV grant for Guinea with the Ministry of Public Health as a new PR
Global Fund grants to Guinea, which are managed under the Additional Safeguard Policy, face numerous challenges. The Global Fund Board has approved an HIV grant with a new principal recipient, the Ministry of Health. The grant complements a TB/HIV grant approved in December 2017.
Tanzania's TB/HIV funding request to the Global Fund yields three grants
The Global Fund Board recently approved three TB and HIV grants for Tanzania, two of which have a government principal recipient (the Ministry of Finance and Planning). The third PR is AMREF Health Africa. The Technical Review Panel cited numerous strengths in the funding request, including the fact that the request identified key populations for TB: i.e. HIV-positive adults and children, mining communities, elderly persons, prisoners, people with diabetes, people who inject drugs, health workers and people living in urban slums.
5. PROFILE
Kenya Red Cross Society has been a successful Global Fund PR
Since the Kenya Red Cross Society became a principal recipient for an HIV grant in 2011, the grant has been consistently rated A1 or A2. This article describes the reasons for the society's success.
Evaluation describes France's 5% Initiative for Global Fund grant recipients as "creative" and "relevant"
An evaluation of France's 5% Initiative says that it "is relevant in the context of specific difficulties linked to the implementation of Global Fund grants in the French-speaking region." The evaluation also refers to the initiative as "a creative mechanism combining a bilateral approach within a multilateral framework." At the same time, evaluators called for some improvements in the operations and oversight of the initiative.
As Global Fund multi-country grants enter a new phase, we map all ongoing and planned regional and multi-country grants
There will be 16–19 multi-country grants from catalytic funding for 2017–2019, fewer than the 24 regional grants from 2014–2016 that are still active. We provide a mapping.
A Global Fund multi-country program in Southeast Asia helps countries SHIFT towards sustainable HIV financing
SHIFT is a two-year regional advocacy program in Southeast Asia that aims to empower civil society organizations and key population communities to advocate for sustainable HIV financing. The four countries are Malaysia, Indonesia, the Philippines and Thailand, all of which have started to plan for transition away from Global Fund support.
9. OF INTEREST
Malaria in Nigeria; the Global Fund and "big alcohol"; and Gender-transformative programming
In this "OF INTEREST" article, we draw attention to an interview on the financial gap for tackling malaria in Nigeria; another article about the Global Fund's partnership with Heineken; and a guide on gender-transformative programming developed by the International HIV/AIDS Alliance.
But problems remain; and some mitigation measures need more time to become effective
There have been significant improvements since the last audit, but there are still many problems that need to be resolved, the Office of the Inspector General (OIG) says, referring to a follow-up audit of Global Fund grants to Nigeria recently completed. Some of the risk mitigation measures that have been implemented need more time to become effective, the OIG added.
A report on the follow-up audit was published in 16 February. The previous audit was conducted in 2015.
This article provides a summary of the OIG report. It is divided into the following sections (the links take you directly to each section):
Achievements and good practices
Key issues and risks
The feedback section contains comments on the audit from some of the organizations mentioned in the OIG's report.
The follow-up audit covered the period from July 2016 to September 2017.
The Global Fund considers Nigeria to be a "mission-critical country." At $674.7 million, Nigeria's 2017–2019 allocation was the largest of any country. Since 2003, the Global Fund has committed over $2.0 billion to Nigeria and disbursed over $1.8 billion. See Table 1 for a list of the grants that were active at the time of the audit.
Table 1: Active Global Fund grants to Nigeria at the time of the audit ($ million)
Principal recipient Comp. Grant name Signed amount
Association for Reproductive and Family Health ** HIV NGA-H-ARFH 7.9 m
Family Health International 360 *** HIV NGA-H-FHI360 101.4 m
Lagos State, Federal Republic of Nigeria * HIV NGA-H-LSMOH 9.6 m
National Agency for Control of AIDS * HIV NGA-H-NACA 138.2 m
Society for Family Health ** HIV NGA-H-SFHNG 35.0 m
Catholic Relief Services *** Malaria NGA-M-CRA 103.1 m
National Malaria Elimination Program * Malaria NGA-N-NMEP 244.8 m
Association for Reproductive and Family Health ** TB NGA-T-ARFH 85.1 m
Institute of Human Virology Nigeria ** TB NGA-T-IHVN 61.0 m
* Government entities ** National NGOs *** International NGOs
Notes: (a) The grants have some activities supporting health systems. (b) All grants had an end date of 31 December 2017. (c) At the time of the audit, no new grants for 2018–2020 had yet been approved.
Just over half of the grant resources are allocated to procuring medicines and other health products.
Nigeria is a lower-middle-income country with a population of 184 million people, the highest in Africa. Nigeria has a three-tier system of government, composed of the federal government, 36 states and 774 local government areas. The country has a multi-ethnic and culturally diverse society. With an abundance of natural resources, Nigeria is Africa's biggest oil exporter and it also has the largest natural gas reserves on the continent.
Nigeria has the highest malaria burden in the world; the second highest HIV burden; and it is one of the top ten countries with the highest TB burden.
Nigeria ranked 152nd out of the 188 countries in the 2016 UNDP's Human Development Index report. Transparency International's 2016 Corruption Perceptions Index ranked Nigeria 136th out of 176 countries. Nigeria continues to face security challenges in the northern states, which affect the implementation of grant activities.
Nigeria's grant portfolio has had more than its share of problems. Part of the country is classified as a challenging operating environment; and Nigeria's grants are being managed under the Additional Safeguard Policy (ASP).
Despite the challenges, Nigeria has made progress against the three diseases. Programs supported by the Global Fund have saved the lives of 1.7 million people as of end 2016. Between 2000 and 2016, deaths from malaria dropped by 43%. Incidence of HIV declined by 37% between 2000 and 2016. With the support of the Global Fund, Nigeria passed the one million mark for people on antiretroviral therapy (ART) in 2017. In addition, in 2017, the Fund financed the distribution of 14 million mosquito nets in six states over a five-month period, covering an estimated 28 million beneficiaries.
Table 2 lists the three areas assessed in the audit, and the OIG's ratings and summary comments for each area.
Table 2: Nigeria audit findings at-a-glance
AREA 1: Effectiveness and efficiency of grant oversight and program management structures
Rating: Partially effective
OIG comments: The increase in the size of the country team as well as the quarterly program reviews have resulted in improved grant oversight. The changes in the implementation arrangements have improved the management of the HIV grant but there are gaps under the malaria grant.
AREA 2: Effectiveness and efficiency of assurance framework and anti-fraud measures
OIG comments: The overall assurance framework has improved with a balance between prevention and detection measures. However, the Fiscal Agent, who is a key mitigation measure is not consistently effective. There are also opportunities to improve efficiency in assurance arrangement. The Global Fund has instituted antifraud measures since the last audit but it is too early to be able to evaluate their impact.
AREA 3: Effectiveness of the supply chain mechanism to deliver and account for medicines procured under the funded programs
Rating: Partially effective.
OIG comments: There have been improvements in inventory management, availability and accountability of medicines across the supply chain. However, challenges in underlying data, roles and responsibility between the service provider and principal recipient, and the Secretariat's management of the service provider require improvement.
The OIG has a four-tiered rating scheme, as follows: Effective; partially effective; needs significant improvement; ineffective.
The OIG identified the following achievements and good practices:
Increased resources to manage the Nigeria portfolio. The number of staff in the Secretariat assigned to the Nigeria portfolio has increased from nine to 19 since the 2015 audit, the OIG reported. In addition, the country team has instituted quarterly programmatic reviews to discuss grant implementation and related challenges with in-country stakeholders.
Improved implementation arrangements for the HIV program. The OIG said that the appointment of Family Health International 360 (FHI360) as a new principal recipient (PR), to assume responsibility for many of the activities previously managed by the National Agency for the Control of AIDS (NACA), has improved the function of the HIV program. Awarding a grant to Lagos State, as a pilot project, the OIG stated, is another positive development. The grant was signed in January 2017 but experienced delays due to challenges in disbursements at the state level. More time is needed for this grant to achieve its full potential, the OIG said.
Strengthened financial management and assurance. The Secretariat has improved how fiduciary risks are managed, the OIG said, and has "generally found the right balance between prevention and detection controls." In addition, the OIG said, the Secretariat has enhanced coordination among assurance providers; has developed risk and control matrices; and has streamlined and enhanced external audit arrangements. Anti-fraud measures have improved since the 2015 audit, the OIG said. The Secretariat revised the fiscal agent's terms of reference, which has resulted in the addition of fraud specialists to the fiscal agent's team. More time is needed to measure the effectiveness of the anti-fraud measures, the OIG stated.
Improved supply chain activities at the central level. The Global Fund has implemented measures which have resulted in improved storage, inventory management and accountability for medicines at the central warehouse.
The audit report described several concerns, including the following:
there are challenges in the implementation arrangements, particularly with respect to the malaria grant;
improvements are needed in program oversight, coordination and assurance;
there are weaknesses in the activities of the fiscal agent;
anti-fraud measures require more time to be effective; and
the supply chain is not yet fully effective and efficient.
Below, we summarize the audit findings related to each of these concerns. (The above links take you directly to the relevant section.)
Implementation arrangements
The audit found that although the Global Fund has made significant changes in the implementation arrangements for the HIV program to address the weaknesses identified in the 2015 audit, there are gaps in the implementation of the malaria program due to capacity constraints of a new PR, Catholic Relief Services (CRS). The grant managed by CRS had been reprogrammed to focus on bed net distribution for six states in 2017.
CRS had limited experience in managing such a large grant in Nigeria and had only 12 months to get the job done, the OIG said. The anticipated support by its regional and global offices that have experience in bed net distribution did not materialize. This resulted in delays which the OIG said had to be mitigated by the country team and in-country partners by hiring a local NGO, the Society for Family Health, to manage distribution in two states. The OIG acknowledged that all 14 million bed nets were distributed in 2017.
In addition, the OIG explained, CRS had planned to implement three of the six mass distribution campaigns through the use of mobile technology –– which was one of the reasons CRS was selected. However, the technology could not be used for any of the campaigns even though about $3.0 million was spent on procuring mobile phones and related equipment. The problem was caused by inconsistencies in the description of the devices in the PR's request for a customs waiver, which resulted in the authorities confiscating the devices for five months. The plan is to use the technology during the next grant period. In addition, the implementation arrangements for the next grant period have been revised: Three new sub-recipients (SRs) will be engaged.
Regarding the grant to Lagos State, the OIG said that although the state model is a laudable approach, it presents unique challenges that need to be continuously monitored and mitigated. For example, the OIG said, there were delays in disbursements. Funds received from the Global Fund in February 2017 could not be used by the PR until April 2017 due to protracted approvals at the state level. This delayed the recruitment of key staff.
The engagement of international NGOs as PRs is expected to improve management of the grant and the timely implementation of activities. The OIG acknowledged that there was an urgent need to get implementation on track. However, the OIG said, there is also a need to build the capacity of the states' disease programs to ensure sustainability. The OIG noted that the states have responsibility over the health facilities due to the federal structure of the country, and that this limits the ability of PRs at the central level to have leverage at the lower level of implementation.
Program oversight
The Secretariat has improved the portfolio's programmatic assurance framework, the OIG said; however, further enhancements are required in program oversight and assurance at country level, and in management of the portfolio by the Secretariat.
At the country level, the OIG said, there is currently no guidance on the role of the country coordinating mechanism (CCM) in countries under the ASP, especially when new PRs are selected by the Secretariat. In Nigeria, the two new PRs were engaged by the Secretariat, which limits the ability of the CCM to hold them accountable. In addition, the OIG said, conflict of interest and capacity constraints have negatively affected CCM performance.
Further, the OIG noted, the national programs were not able to conduct programmatic oversight of the activities implemented by NGOs because their travel-related activities were suspended in April 2016 when disbursements for Nigeria's HIV and malaria grants were halted (see GFO article) and, subsequently, proposed budget amounts for oversight by the national programs were not approved. (Disbursements resumed for the malaria grant in May 2017, and for the HIV grant in November 2017.)
The audit identified problems with the review of documents submitted to the Secretariat by implementers, especially for the TB grants, the OIG revealed. Some of the problems related to the poor quality of the documents, but there were also delays in the response of the Secretariat to requests from the country. The OIG noted that the TB program is significantly behind schedule in achieving its targets.
Agreed management action
The Secretariat will submit revised guidance on CCM roles and responsibilities for countries under the ASP. Based on the approved guidance, the Secretariat will set specific expectations for the Nigeria CCM.
Due date: 31 December 2018
Fiscal agent
The audit found that the fiscal agent's reviews are not consistently effective and efficient due to gaps in its quality assurance process and the Secretariat's oversight. Although the fiscal agent is a critical component of the risk mitigation measures for the portfolio, the OIG said, the agent does not consistently identify material gaps in controls and payments requests from the implementers. In addition, there are delays in the agent's review of the payment requests due to gaps in the quality of documents submitted by implementers and inefficiencies in the agent's processes.
The OIG said that there is a need to reassess the balance between financial assurance and program implementation. The fiscal agent currently reviews all transactions at selected implementers regardless of the amounts involved. The OIG said that 26% of the transactions were below $250.
In addition, the current assurance framework requires third-party supporting documentation for the $100-a-month payments to each of 106 community-based organization (CBO) implementers. The OIG said that this money goes into a pool of resources to support the CBOs, which makes it difficult for them to allocate the supporting documentation specifically to the Global Fund grant. This has delayed implementation of activities by the CBOs. The OIG said that the country team had identified the problem and had considered potential mitigation measures, including those suggested by the fiscal agent, but the Secretariat decided not to take any action.
The OIG said that the gaps in the performance of the fiscal agent can be attributed to:
limited independent review of the work performed by the fiscal agent's staff;
inconsistent use by the agent's staff of existing checklists for the review of transactions and month-end controls;
no formal induction program and ongoing development for the agent's staff; and
the lack of systems and tools for the Secretariat to evaluate the performance of fiscal agents.
The Secretariat will:
review the terms of reference of the fiscal agent to identify areas where the agent can be more efficient and effective;
implement a quality assurance and monitoring system; and
develop a corporate approach on the performance management of fiscal agents.
Due date: 31 March 2019
Anti-fraud measures
The audit found that the Secretariat has significantly improved the management of the risk of fraud in the Nigeria portfolio, but that more time is needed to fully evaluate the impact of these efforts.
Following the 2015 audit, and an independent financial control review conducted by a public accounting firm in 2016, the terms of reference of the fiscal agent were revised to incorporate fraud prevention and detection measures. This resulted in the addition of fraud specialists to the fiscal agent's team, the OIG reported.
The fraud specialists have supported the PRs in developing comprehensive anti-fraud policies and procedures, including internal mechanisms for reporting suspected fraud, the OIG said. For most of the PRs, fraud risk registers have been developed that identify and address gaps in controls. The non-fraud specialists in the fiscal agent's team and internal audit units of the PRs are being trained on fraud risks and provided with fraud tools, the OIG stated.
Although there have been improvements in fraud prevention, the OIG said, there is a need to improve fraud detection and reporting.
The audit found that the Secretariat is addressing the supply chain challenges identified in the 2015 audit. Hiring Chemonics to manage the storage and distribution of HIV and malaria medicines on behalf of the PRs has improved storage, inventory management and accountability for medicines at the central and zonal warehouses, the OIG said. In addition, the Global Fund is working with in-country partners and the government to integrate the existing vertical supply chain systems under the National Supply Chain Integration Project.
As well, the OIG said, medicines and health products received from the Global Fund's Pooled Procurement Mechanism can be reconciled and traced; storage conditions and practices at the central level were in accordance with World Health Organization (WHO) guidelines; and TB and multi-drug-resistant TB medicines are also appropriately managed by the Association for Reproductive and Family Health and the Institute of Human Virology Nigeria.
Despite this progress, the OIG said, several challenges remain. Specifically:
Gaps in distribution arrangements. There are gaps in delineating the roles and responsibilities of the PRs and Chemonics. During the January 2017 distribution cycle, an incomplete request from the PRs left more than 40 primary health care facilities in Kano State without rapid diagnostic kits for 30 days. At the same time, Chemonics did not consistently distribute the requested medicines to the facilities; some get more than what they requested, others less.
Weak management of expired medicines. This was a problem in the 2015 audit and, despite some improvements, it remains a problem. In the five warehouses managed by Chemonics, the OIG estimated that 1,580 cubic meters of space (approximately 1,090 pallets) was being occupied by expired medicines. The Global Fund is being charged, on average, $84,000 a year for warehousing expired products. All seven health facilities visited by the OIG had expiries which have taken over some storage space (e.g. about 40% of the space in the Rainbow Hospital and Maternity facility). Subsequent to the audit, the Secretariat has incorporated waste management in its contract with Chemonics to enable it to retrieve expired medicines from the health facilities for destruction.
Inadequate inventory management practices at facility level. Although significant improvements have been made at the central level, the same cannot be said for the facility level. However, the OIG acknowledged that the government and partners have key roles to play in addressing inventory challenges at the health facilities.
Delays in customs clearance. If not addressed, these delays could result in stock-outs. There was a stock-out of anti-malaria medicines and commodities at the central level in 2017 for a period of four months, which triggered emergency procurement by the Global Fund.
Secretariat's monitoring of Chemonic's performance inadequate. The key performance indicators (KPIs) related to warehousing are adequate, but the distribution KPIs cover only "on time" and not "in full." Subsequent to the audit, the Secretariat revised the distribution KPIs.
The Secretariat will clarify the roles and responsibilities of the PRs and Chemonics in the distribution process and will conduct a dissemination session to ensure that relevant parties understand their role in the process.
Due date: 30 June 2018
The OIG identified gaps in internal controls on the quality of data in the health facilities, which was also an issue in 2015 audit. The OIG acknowledged that this is a national challenge, and that more time and joint efforts from all stakeholders are required to address the problem. "Progress in this area is also highly contingent on the Government of Nigeria and its willingness to increase the level of its investments in health systems," the OIG observed.
The OIG said that there have been delays in the roll-out of the Strengthening National Health Management Information System project –– delays that were due to the suspension of grant activities in 2016 and subsequent challenges in recruiting a technical service organization to lead the roll-out.
The OIG reported that during the planning phase of this follow-up audit, the Secretariat acknowledged that the data quality challenges at health facilities are yet to be resolved. Given the lack of progress on this issue, the OIG said, it has not performed additional work as part of the audit.
The OIG indicated that the government has refunded the $5.8 million in recoverable amounts identified from previous OIG audit and investigations.
Message from the Interim Executive Director
In a message from the Interim Executive Director, which was included in the audit report, Marjorie Wijnroks said:
"This follow-up audit report clearly demonstrates that the Global Fund, together with its country partners, have achieved rapid and significant progress since 2015, when a previous audit was conducted. The portfolio is now managed under a strengthened risk management and assurance framework and is on a better trajectory for enabling the country to deliver improved programmatic results. The audit takes a sharp view of progress in the areas where deficiencies were previously identified and highlights some specific gaps and key areas requiring further improvement. The Secretariat is already taking responsive action that will further improve grant implementation."
Wijnroks said that in response to challenges described with the malaria grants, the Secretariat and the PRs have revised the implementation arrangements for 2018–2020, including the engagement of experienced SRs…. "As a result of this proactive engagement, all 2017 objectives for the malaria program were fully met," she stated.
Wijnroks said that the Global Fund now has significantly greater assurance that medicines and other health products are available to patients when and where they need them –– thanks partially to the establishment of 37 logistics coordination management units, one in each state, which focus on improving timeliness and accuracy of supply chain data. "We also repositioned short-dated TB and malaria medicines and other health commodities, resulting in the use of life saving commodities that would otherwise [have] been at risk of expiry," Wijnroks said.
On 13 December, the Board approved two malaria grants to Nigeria (see GFO article). The CCM is expected to submit a revised TB/HIV funding request in Window 5, on 30 April 2018; the Technical Review Panel had recommended that the original request, submitted in Window 2 in May 2017, be sent back for iteration.
We provided organizations mentioned in the OIG's report with an opportunity to comment on the report's findings. The following responses were received.
Family Health International 360 (FHI360)
Satish Raj Pandey, Acting Country Director for FHI360 in Nigeria, said that FHI360 agreed with the wording of the OIG report in most of the sections where FHI360 was mentioned. However, he said, FHI360 disagrees with the wording of section1.3 of the OIG's report, which is about data quality. "Though we know that there are still some challenges in data quality, a lot of progress has been made on this issue under FHI360 leadership as at the time of the OIG audit," Pandey said. Pandey provided the following examples of progress:
FHI360 Global Fund project transition from the inherited Microsoft Excel–based reporting to electronic platform (DHIS) that reduces data entry error and promotes timely reporting of program achievement across supported entities. This is evident in the three of our program areas (HIV counselling and testing, PMTCT, ART) which had an over 90% reporting rate as at the time of the OIG review.
Implementation of the LFA data quality audit recommendations: Part of FHI360's effort prior to OIG audit in 2017 was ensuring adequate supply of M&E tools to the service delivery points in response to tools shortage at service delivery points (SDPs) as identified by the LFA. All the newly revised national [tools] were printed, distributed to SDPs; and the capacity of the healthcare workers in the SDPs built on these tools.
Quarterly conduct of data verification and quality assessment exercises were carried out. Data verification exercises were conducted four times during the life of the project. Three were conducted before the OIG audit period. Action points were developed from these exercises and management letters sent to defaulting SRs.
Editor's note: A spokesperson for the OIG told Aidspan that there may have been a misunderstanding: The finding in Section 1.3 that Pandey is referring to, he said, did not relate to FHI 360's work but to the data quality at a national level. "This finding has also been communicated to the country and all stakeholders throughout the reporting process and acknowledged by the country coordinating mechanism, headed by the Minister of Health," the spokesperson said.
The relevant text in Section 1.3 of the OIG's report reads as follows:
"Data quality remains a challenge on the portfolio. A significant issue identified in the previous OIG audit that still remains largely outstanding relates to the gaps in the internal controls over data quality across the health facilities. This was partly because relevant data registers were either not available or not appropriately used. The supervision and related controls over programmatic data had also been found inadequate by the OIG in 2015. The OIG acknowledges that this is a national challenge, and more time and joint effort from all stakeholders are required to be able to address data quality issues. Progress in this area is also highly contingent on the Government of Nigeria and its willingness to increase the level of its investments in health systems."
Rebecca Hallam, CRS Country Representative for Nigeria, provided Aidspan with the following statement:
"Catholic Relief Services (CRS) appreciates the opportunity to share reflections following the recent release of a report by the OIG on Nigeria. CRS expresses full support of the OIG, and values the collaboration we have had this past year, specifically on strengthening fraud management systems as well as audit consultations on the performance of the Global Fund malaria grant in Nigeria. CRS is proud of the success of this one-year project –– valued at $103m plus $40m in bed nets –– launching the initiative in a very short time frame, in a complex context and environment. We met the challenge expressed by the Global Fund Secretariat to prioritize this grant as an institution, and CRS executives and field leadership embraced an all-agency approach. We mobilized many headquarters, regional and global experts and management staff who worked for months in-country with existing and newly-hired staff up to launch project activities. All efforts were made to engage stakeholders, plan jointly, identify viable logistics and warehousing arrangements, and also explore local institutions to carry out key activities where capacity existed (e.g. with Society for Family Health [SFH], for bed net distributions).
"The results speak for themselves: As a new PR in the country, CRS quickly built strong relationships with the National Malaria Elimination Programme (NMEP), Ministry of Health leadership and staff, state governors, civil society and faith-based leaders; and all came together to successfully distribute 14 million bed nets over a five month period. All parties –– including the Nigerian Government and the Global Fund Secretariat –– have expressed a high level of satisfaction in the project's achievements and results which benefitted nearly 28 million Nigerian women, men and children. CRS congratulates all government and non-government partners for making a challenging transition, embracing new roles and responsibilities, and overcoming new obstacles.
"CRS is honored to be selected as PR for the 2018–2020 malaria grant –– jointly with NMEP –– and looks forward to working closely with the Nigerian government, the CCM, the Global Fund Secretariat, and all local partners and stakeholders in executing the grant in a successful and efficient manner; and continuing to work openly and productively with the OIG."
Society for Family Health (SFH)
We received feedback from Bright Ekweremadu, a spokesperson for SFH. In the section of our article on implementation arrangements, we mention that the country team and in-country partners hired a local NGO, the Society for Family Health, to manage distribution of bed nets in two states. Bright said that SFH was hired "as a result of its demonstrated experience and strong capacity in the area of malaria programming in Nigeria and in particular its experience in mass campaign for nets."
Dr Dayo Lajide, Grant Management Unit Coordinator for the Ministry of Health for Lagos State, commented on some text in the section of this article on implementation arrangements. Summarizing what was written in the OIG report, the text said that funds received from the Global Fund in February 2017 could not be used by the PR until April 2017 due to protracted approvals at the state level; and that this delayed the recruitment of key staff. Dr Lajide said that the last part of the text should have read as follows: "This delayed the full implementation of grant activities by the LSMOH Grant Management Unit."
Do you have any reaction to this article (or any article in GFO)? To send a note to the editor, just click here. We value your feedback.
country coordinating mechanism
Read this article in French. Lire l'article en français.
< Previous Article in Issue
Next Article in Issue >
Endorsements and Outcomes
Other news relating to the Global Fund partnership
Kenyan High Court upholds criminalization of same-sex relations
Copyright © 2002-2018 Aidspan | Privacy-policy | Sitemap


text:
Q: Adding table to existing map layer in ArcGIS Online I have a map service that is published to a local ArcGIS Server. I've added it as a service to ArcGIS Online and added it to a map and made a lot of changes to the searching, pop-up's, etc. Later, I went back to the MXD and added a new table that is referenced by another layer. When I go back to the map in ArcGIS Online, it does not show the table I added. However, if I start a new map and add the service, the new table is picked up. How can I add that one table to the existing map without having to delete the layer and add it back? I really don't want to have to set up the map over again every time I need to add a layer.

A: you need to override the existing service by re-sharing the service then use the overwrite option. That way the new service will include your newly added table.

redpajama_set_name: RedPajamaStackExchange


text:
TwitterFacebookTumblr
For the Press, Bloggers, Hacktivists, and others
Why These Articles?
Engineering Evil
Intel Portal for Weighted Data and Information
Monsanto and others conspired with an Army experiment to secretly poison people with toxic chemicals, a class action claims in City Court.
By Ralph Turchiano on January 5, 2015
Requested Repost. Articles will be held at my sister site EVESDRIFT
Army Poisoned People in '50s, Class Claims
By JOE HARRIS
ST. LOUIS (CN) – Monsanto and others conspired with an Army experiment to secretly poison people with toxic chemicals in a giant segregated housing complex in the 1950s, a class action claims in City Court.
Lead plaintiff Benjamin Phillips Sr. claims defendants Monsanto, Parsons Government Services and SRI International participated in a study beginning in 1953 that lasted into the 1960s.
Phillips claims the study, the "Involuntary Chemical Study on PI Residents" or "ICS", was conducted around the Pruitt-Igoe housing complex in St. Louis.
"This study consisted generally of the following: defendants, along with other known conspirators such as the United States Army) and unknown conspirators caused to be sprayed upon the residents and structures of PI chemicals, such as cadmium, including potentially radioactive cadmium, with the knowledge or consent of those resident, the administrators of PI or city or other government officials. The purpose of this study is unknown," the complaint states. (Open parentheses in complaint.)
Phillips, who lived at Pruitt-Igoe at the time, claims the chemicals caused emotional psychological trauma and harm as well as personal injury.
He seeks actual and punitive damages for public nuisance, liability, intentional infliction of emotional distress and battery. He is represented by Elkin Kistner, with Bick & Kistner.
The 33, 11-story buildings in the Pruitt-Igoe complex were torn down in the 1970s after the place became famous for its poverty, crime and segregation.
http://www.courthousenews.com/2012/10/30/51794.htm
Revealed: Army scientists secretly sprayed St Louis with 'radioactive' particles for YEARS to test chemical warfare technology
By Emily Anne Epstein
PUBLISHED:09:16 EST, 29 September 2012| UPDATED:11:21 EST, 29 September 2012
The United States Military conducted top secret experiments on the citizens of St. Louis, Missouri, for years, exposing them to radioactive compounds, a researcher has claimed.
While it was known that the government sprayed 'harmless' zinc cadmium silfide particles over the general population in St Louis, Professor Lisa Martino-Taylor, a sociologist at St. Louis Community College, claims that a radioactive additive was also mixed with the compound.
She has accrued detailed descriptions as well as photographs of the spraying which exposed the unwitting public, predominantly in low-income and minority communities, to radioactive particles.
Test: Sociologist Lisa Martino-Taylor, right, a sociologist at St. Louis Community College, has spent years tracking down declassified documents to uncover the lengths which the US experimented on people without their knowing. At left, cadmium sulfide, the 'harmless' chemical sprayed on the public is pictured
Spray: She has accrued detailed descriptions as well as photographs of the spraying, which took place as part of Manhattan-Rochester Coalition, which was an operation that dispersed zinc cadmium silfide particles over the general population, a compound that was presented as completely safe
'The study was secretive for reason. They didn't have volunteers stepping up and saying yeah, I'll breathe zinc cadmium sulfide with radioactive particles,' said Professor Martino-Taylor to KSDK.
Through her research, she found photographs of how the particles were distributed from 1953-1954 and 1963-1965.
In Corpus Christi, the chemical was dropped from airplanes over large swathes of city. In St Louis, the Army put chemical sprayers on buildings, like schools and public housing projects, and mounted them in station wagons for mobile use.
Despite the extent of the experiment, local politicians were not notified about the content of the testing. The people of St Louis were told that the Army was testing smoke screens to protect cities from a Russian attack.
'It was pretty shocking. The level of duplicity and secrecy. Clearly they went to great lengths to deceive people,' Professor Martino-Taylor said.
Controversial: But Professor Martino-Taylor says that it wasn't just the 'harmless' compound, radioactive particles were also sprayed on the unwitting public. A woman refills the spray canisters in this archive picture
Scope: In St Louis, the Army put chemical sprayers on buildings, like schools and public housing projects, and mounted them in station wagons for mobile use
She accrued hundreds of pages of declassified information, which she has made available online.
In her research, she found that the greatest concentration of spraying in St Louis was at the Pruitt-Igoe public housing complex, which was home to 10,000 low income residents. She said that 70 per cent of those residents were children under the age of 12.
Professor Martino-Taylor became interested in the topic after hearing independent reports of cancers among city residents living in those areas at the time.
'This was a violation of all medical ethics, all international codes, and the military's own policy at that time,' said Professor Martino-Taylor.
How To: Despite the extent of the experiment, local politicians were not notified about the content of the testing. In this picture, a man demonstrates how to spray the canisters
School: The people of St Louis were told that the Army was testing smoke screens to protect cities from a Russian attack. A canister is positioned on top of a school in this photo
'There is a lot of evidence that shows people in St. Louis and the city, in particular minority communities, were subjected to military testing that was connected to a larger radiological weapons testing project.'
Previous investigations of the compound were rebuffed by the military, which insisted it was safe.
However, Professor Martino-Taylor believes the documents she's uncovered, prove the zinc cadmium silfide was also mixed with radioactive particles.
She has linked the St Louis testing to a now-defunct company called US Radium. The controversial company came under fire, and numerous lawsuits, after several of its workers were exposed to dangerous levels of radioactive materials in its fluorescent paint.
Contaminated: The Army has admitted that it added a fluorescent substance to the 'harmless' compound, but whether or not the additive was radioactive remains classified
Exposed: In her research, she found that the greatest concentration of spraying in St Louis was at the Pruit-Igoe public housing complex, which was home to 10,000 low income residents. She said that 70 per cent of those residents were children under the age of 12
'US Radium had this reputation where they had been found legally liable for producing a radioactive powdered paint that killed many young women who painted fluorescent watch tiles,' said Professor Martino-Taylor.
In her findings, one of the compounds that was sprayed upon the public was called 'FP2266', according to the army's documents, and was manufactured by US Radium. The compound, also known as Radium 226, was the same one that killed and sickened many of the US Radium workers.
The Army has admitted that it added a fluorescent substance to the 'harmless' compound, but whether or not the additive was radioactive remains classified.
Professor Martino-Taylor has not been able to find if the Army ever followed up on the long term health of the residents exposed to the compound. In 1972, the government destroyed the Pruitt-Igoe houses.
Upon learning of the professor's findings, Missouri lawmakers called on the Army to detail the tests.
'I share and understand the renewed anxiety of members of the St. Louis communities that were exposed to the spraying of (the chemicals) as part of Army tests during the Cold War,' Senator Claire McCaskill wrote to Army Secretary John McHugh.
'The impacted communities were not informed of the tests at the time and are reasonably anxious about the long term health impacts the tests may have had on those exposed to the airborne chemicals.'
Senator Roy Blunt called the findings 'absolutely shocking.'
'The idea that thousands of Missourians were unwillingly exposed to harmful materials in order to determine their health effects is absolutely shocking. It should come as no surprise that these individuals and their families are demanding answers of government officials,' Senator Blunt said.
Read more: http://www.dailymail.co.uk/news/article-2210415/Revealed-Army-scientists-secretly-sprayed-St-Louis-radioactive-particles-YEARS-test-chemical-warfare-technology.html#ixzz27ujqlusB Follow us: @MailOnline on Twitter | DailyMail on Facebook
Categories: Societal
Would the Stress Vaccine Change Behavior and Moral Judgment?
Prince Andrew named in child sex slave case
Top Trending Articles (Last 48 hours)
Adult Friend Finder Website Hacked: How To Search The Leaked Database Of Emails And Usernames For The Adult Dating Site
Former Justice Souter: 'Pervasive civic ignorance' in U.S. could bring dictatorship
Software that tracks people on social media created by defence firm
Goldman Sachs made more money from its investment banking division in 2013 than any point in its 145-year history (except 2007 when the credit crunch hit)
The Bank of America Keyword list is confirmed ( Hundreds of Classified Project Titles )
Recent Posts: ClinicalNews.Org
Gut bacteria could guard against Parkinson's, study finds
Egg-based flu vaccines: Not all they're cracked up to be?
Could pancreatitis be a stress hormone deficiency?
Mutagenesis – Biowarfare – EVES Drift: EVES Drift
Copper nanoparticles and immunotherapy rapidly eliminate cancer cells – Pilot Study
Children's Hospital Colorado uncovers largest US outbreak of neurologic disease to date
Eating Chili Peppers reduced all cause Mortality rates by 23%
DNA discovered not to be a good predictor of health
Engineering Evil Tweets
Now it just looks too easy 🤗;#🐅🐺🐅 #moreanimalthanhuman #fitnessselfie #fitness #mutant #alwaysevolving #cyberwolf… twitter.com/i/web/status/1….....Please No Advertising	42 minutes ago
Follow @RalphTurchiano
EngineeringEvil
Traffic Velocity
Top categories: Societal National Security Agency