text:
Polar Bears: A Summer Odyssey
Leaving Neverland Part Two
Pharsalus
Winter on Fire
Inside the Medieval Mind: Knowledge
One Life on the Limit
Ape Man: Search for the First Human
The Nazis, A Warning From History. Episode 2
Reel Rock 10
Fire Ants The Invincible Army
"The Universe" Sort by
What is our future
Professor Brian Cox concludes his exploration of our place in the universe by asking what next for the ape that went to space. Our future is far from certain. In Florida, Brian joins the latest efforts to protect Earth from potential catastrophic events. He joins a team of Nasa astronauts who are training for a future mission to an asteroid - should we ever discover one coming our way - under 30 feet of water in a submerged laboratory that simulates space. It is just one example of how, for our long-term survival, space exploration may well be vital. It is a view shared by Apollo 16 astronaut Charlie Duke, who tells Brian what it was like to escape the confines of the planet. It is a dream that both Nasa and now commercial companies share as they race to get humans back into deep space.
But space travel, like every leap our civilisation has ever made, requires energy. Here too, scientists are hard at work attempting to safeguard our future. At the National Ignition Facility in California, Brian witnesses the world's most successful fusion experiment in action. He believes that if their mission succeeds, our civilisation will have unlocked a way to the stars that will not destroy the planet in the process. Brian concludes by returning to the top of the world in Svalbard, where he gains access to our civilisation's greatest treasure, locked away in a vault buried deep in the permafrost.
Series: Human universe
Weirder and Weirder
Dr Hannah Fry explores a paradox at the heart of modern maths, discovered by Bertrand Russell, which undermines the very foundations of logic that all of maths is built on. These flaws suggest that maths isn't a true part of the universe but might just be a human language - fallible and imprecise. However, Hannah argues that Einstein's theoretical equations, such as E=mc2 and his theory of general relativity, are so good at predicting the universe that they must be reflecting some basic structure in it. This idea is supported by Kurt Godel, who proved that there are parts of maths that we have to take on faith.
Hannah then explores what maths can reveal about the fundamental building blocks of the universe - the subatomic, quantum world. The maths tells us that particles can exist in two states at once, and yet quantum physics is at the core of photosynthesis and therefore fundamental to most of life on earth - more evidence of discovering mathematical rules in nature. But if we accept that maths is part of the structure of the universe, there are two main problems: firstly, the two main theories that predict and describe the universe - quantum physics and general relativity - are actually incompatible; and secondly, most of the maths behind them suggests the likelihood of something even stranger - multiple universes.
We may just have to accept that the world really is weirder than we thought, and Hannah concludes that while we have invented the language of maths, the structure behind it all is something we discover. And beyond that, it is the debate about the origins of maths that has had the most profound consequences: it has truly transformed the human experience, giving us powerful new number systems and an understanding that now underpins the modern world.
Series: Magic Numbers
Nature Great Events
The Nazis, A Warning From History

redpajama_set_name: RedPajamaCommonCrawl


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text:
/**
 * Yaml wrappers, errors and utilities.
 */
package org.mapfish.print.wrapper.yaml;

redpajama_set_name: RedPajamaGithub


Listen Do college sports need to be saved?
If you missed this week's Midmorning program on a new article trashing the NCAA's treatment of college athletes, here's a link to the audio. It's a big topic, and I'll post the highlights later today.
Update: Here's a rough summary of the discussion.
Newer › Midmorning: Should college athletes be compensated more?


text:
\section{Introduction}

Cosmological observations suggest that about ninetysix percent of the present energy density in the universe resides in forms unknown to the standard
model of particle physics. Measurements of the fluctuations in the cosmic microwave background (CMB) radiation are consistent with a nearly critical
density universe\cite{Spergel:2003cb}, as predicted by the early inflation. Assuming the validity of general relativity, roughly two thirds of this
density nowadays must be due to a negative-pressure component called dark energy\cite{Peebles:2002gy} (DE) to explain the acceleration of the universe
indicated by distance-redshift curves of the high redshift supernovae\cite{Riess:2004nr}. The rest of the density is in gravitationally clustered
matter with negligible pressure on cosmological scales. However, only a fraction of this matter consists of the (partly luminous) baryonic matter
known to the standard model. Dark matter (DM) is needed for consistency with a convincing number of astrophysical observations, for example the flat
rotation curves of galaxies\cite{Bertone:2004pz}.

It has been proposed that the two dark components do not evolve independently but are non-minimally coupled. Due to their different pressures,
the densities of these components decay with different rates. This rises the disturbing question why they appear to be of the same order of
magnitude right now. An explicit coupling between DE and DM\cite{Wetterich:1994bg} could provide a phenomenological solution to this so called
''cosmic coincidence problem''\cite{Zimdahl:2001ar,Chimento:2003ie,
Bento:2004uh,Cai:2004dk}. On the other
hand, there is theoretical motivation\cite{Farrar:2003uw} to couple
quintessence fields\cite{Zlatev:1998tr,Caldwell:1997ii} to DM (see,
however\cite{Doran:2002bc}). In particular, if
it is held that scalar-tensor theories should be described in the Einstein frame, it follows that
scalar fields with a nonminimal coupling to other matter are general predictions of all dimensionally reduced
theories\cite{Albrecht:2001xt,Brax:2004ym}. In the context of string
theory, the dilaton could be such a field, and indeed has been proposed as a candidate
for DE \cite{Gasperini:2001pc, Bean:2000zm}. Since generally
the dilaton coupling to different matter species could be different\cite{Garcia-Bellido:1992de} and such couplings to baryonic matter are tightly
constrained by high precision solar system tests of general relativity\cite{Damour:1994zq}, it is of interest to concentrate on simpler models where
the dilaton is only coupled to DM, while the possible coupling to baryons is assumed negligible.

This paper concerns the linear perturbations in such models. The purpose is to find how the formation of cosmological structure
in pressureless, dust-like matter is influenced by a coupling to a scalar field, when this coupling is significant already at the background order as
required if it is to address the coincidence problem. First the cosmological field equations for scalar field interacting with DM
are derived to linear order in section II. These equations have been presented in the literature before (for example, see \cite{Amendola:2003wa}), and
the reader familiar with them may skip this section. However, there we hope also to somewhat clarify the relations of different possible
formulations and theoretical frameworks for the coupled dark sector. In the two following sections we investigate
specific cases. The simplest models of interacting DM and DE can be excluded by comparison to the CMB observations\cite{Hoffman:2003ru}, but more
sophisticated scenarios exist\cite{Gasperini:2001pc, Bean:2000zm,Farrar:2003uw}. In
section III we study a model featuring two DM components, only the
subdominant of them interacting with quintessence\cite{Huey:2004qv}. A model where the DE-DM coupling is given by a polynomial function of the DE
field\cite{Bean:2000zm} is considered in section IV. These two models are based on a low-energy limit of effective string theory action and have been
previously shown to naturally lead to a late-time acceleration of the universe. Though the details of the mechanisms are different, the DE
domination in each case is triggered by the time-evolving coupling. Large scale structure in both of the two scenarios have previously been claimed
to fit observations as well as or better than the standard $\Lambda$CDM model. However, here a closer inspection shows that these models are ruled out
because of the excessive DM structure they predict in the late-time universe. In subsection IVB we consider the adiabatic initial conditions in for a
scalar field coupled to DM. In section V we discuss the relation of our results to other models and conclude.

\section{Equations}

\subsection{Field equations and Bianchi identities}

We consider an action of the form

\begin{eqnarray} \label{action}
    \mathcal{S} = \int d^4x \sqrt{-g}[\frac{\kappa^2}{2}R - \frac{1}{2}\partial^\mu\phi\partial_\mu\phi - V(\phi)
                  + \gamma_\chi (\phi)\mathcal{L}^{(\chi )} + \mathcal{L}^{(m)}],
\end{eqnarray}
where $\chi$ stands for an interacting matter species, and $m$ for non-interacting ones. The constant $\kappa \equiv (8 \pi G)^{-1/2}$.
We use the definition
\begin{eqnarray}
    T_{\mu\nu}^{(i)} \equiv -\frac{2}{\sqrt{-g}}\frac{\delta (\sqrt{-g}\mathcal{L}_i)}{\delta(g^{\mu\nu})},
\end{eqnarray}
and the Lagrangian of the field $\phi$ is taken to consist of the two first terms in the action integral Eq.(\ref{action}). The Einstein equations
resulting from this action can be written as
\begin{eqnarray}
    G_{\mu\nu} = \frac{1}{\kappa^2} (T_{\mu\nu}^{(\phi)} + \gamma_\chi(\phi)T_{\mu\nu}^{(\chi)} + T_{\mu\nu}^{(m)}),
\end{eqnarray}
and the equation of motion for the field $\phi$ is
\begin{eqnarray} \label{eom}
    \Box \phi = V'(\phi) - \gamma_\chi'(\phi)\mathcal{L}^{(\chi)}.
\end{eqnarray}
The Bianchi identities then imply
\begin{eqnarray}
    \nabla_\mu {T^{\mu}_\nu}^{(m)}=0,
\end{eqnarray}
\begin{eqnarray} \label{bianchic}
    \nabla_\mu {T^{\mu}_\nu}^{(\chi)}=(\delta^\mu_\nu\mathcal{L}^{(\chi)} -
               {T^{\mu}_\nu}^{(\chi)})\frac{\gamma_\chi'(\phi)}{\gamma_\chi(\phi)}\nabla_\mu\phi.
\end{eqnarray}
Thus the energy momentum tensor for the interacting components are not separately conserved.

From now on we will assume that
\begin{eqnarray} \label{lagran}
\mathcal{L}^{(\chi)} = -\sum_a m_a\delta (x-x_a(t))\frac{\sqrt{-g_{\mu\nu}\dot{x}^\mu\dot{x}^\nu}}{\sqrt{-g}},
\end{eqnarray}
where $|\dot{x}^i| \ll 1$, i.e. the interacting component behaves as dust. This is in fact the case most commonly studied in cosmology (for models
with
DE coupled to neutrinos, see Refs.\cite{Peccei:2004sz,Brookfield:2005td}). One notes that the term $\gamma_\chi(\phi)\mathcal{L}^{(\chi)}$ in the
action
Eq.(\ref{action}) can be naturally interpreted as a Lagrangian for
particles with field-dependent masses, $m_a(\phi) = m_a\gamma_\chi(\phi)$. Such a Lagrangian can follow from a conformal
transformation. Consider a scalar-tensor theory defined by a gravitational Lagrangian proportional to $R/\sqrt{\gamma(\phi)}$. Then
the metric in the Einstein frame is $\hat{g}_{\mu\nu} \equiv g_{\mu\nu}/\sqrt{\gamma(\phi)}$. In terms of this metric, the action
for the Lagrangian Eq.(\ref{lagran}) reads
\begin{eqnarray}
S_\chi = \int d^4x \sqrt{-\hat{g}} \gamma(\phi)\hat{\mathcal{L}}^{(\chi)}.
\end{eqnarray}
(At this point one may have to redefine the field in order to have the canonical kinetic term for the scalar field as in the action
Eq.(\ref{action}).) A more standard way, however, to describe scalar-tensor theories in the Einstein frame is to define the
component
\begin{eqnarray} \label{x-comp}
T_{\mu\nu}^{(X)} = \gamma_\chi(\phi)T^{(\chi)}_{\mu\nu}.
\end{eqnarray}
This energy momentum tensor then depends on the field $\phi$, which turns out to be coupled to the trace $T^{(X)}$. For some
purposes the $\chi$-formulation is more convenient, since there the divergence in Eq.(\ref{bianchic}) vanishes except for the
spatial part in the linear order. However, we will also use the $X$-formulation for some calculations, especially in subsection IIIB.
With the variable mass particle interpretation, the difference is simply that $\rho_\chi$ is proportional to the number density of the DM
matter particles, while $\rho_X$ is their gravitating energy density. The fact that the action Eq.(\ref{action}) is equivalent to the
case of a trace-coupled scalar field and the possibility to make direct contact with conformally transformed scalar tensor and variable mass
particle theories are independent of the form of the coupling. However, it is required that the Lagrangian is effectively of the form
Eq.(\ref{lagran}). From that follows (when $|\dot{x}^i| \ll 1$)
\begin{eqnarray}
\mathcal{L}^{(\chi)}=T^{(\chi)}=-\rho_\chi.
\end{eqnarray}
These simple identities would not, of course, hold for a more general Lagrangian.

\subsection{Cosmological background and perturbations}

We consider a flat FRW universe. Including small perturbations about the background, we can write the line element as
\begin{eqnarray}
      d s^2 = a^2(\tau)[-d\tau^2 + (\delta_{ij} + h_{ij}) dx^i dx^j].
\end{eqnarray}
This parameterisation of the metric perturbations is called the synchronous gauge. There we can characterize the scalar modes of $h_{ij}$ in the
Fourier space as
\begin{eqnarray}
       h_{ij}({\bf x},\tau) = \int d^3k e^{i{\bf k} \cdot {\bf x}} \biggl[\hat{k}_i\hat{k}_jh({\bf k},\tau) \mbox{} +  (\hat{k}_i\hat{k}_j -
                          \frac{1}{3}\delta_{ij})6\eta({\bf k},\tau)\biggr],
\end{eqnarray}
when ${\bf k}=k\hat{k}$. In the following, prime is a derivative with respect to $\phi$, an overdot represents derivative with respect to conformal time
$\tau$,
and $H$
is the conformal Hubble parameter $H \equiv \dot{a}/a$. These and mostly all other notations and conventions are those of Ma and
Bertschinger\cite{Ma:1995ey}. With these, the Friedmann equation reads
\begin{eqnarray} \label{friedmann}
H^2 = \frac{a^2}{3\kappa^2}\left( \frac{\dot{\phi}^2}{2a^2} + V(\phi) + \gamma_\chi \rho_\chi + \rho_m \right),
\end{eqnarray}
while evolution of the scalar field is governed by the equation
\begin{eqnarray} \label{eom2}
\ddot{\phi} + 2H\dot{\phi} + a^2 V(\phi)' = -a^2\gamma_\chi'(\phi)\rho_\chi,
\end{eqnarray}
following from Eq.(\ref{eom}). In addition to the interacting species and the scalar field, we include standard CDM, baryons and radiation in the
universe. Then the energy densities scale as usually, and therefore, with the scale factor normalized to unity today, we may write
\begin{eqnarray}
\rho_\chi=\frac{\rho_\chi^0}{a^3}, \qquad
\rho_c=\frac{\rho_c^0}{a^3}, \qquad
\rho_b=\frac{\rho_b^0}{a^3}, \qquad
\rho_r=\frac{\rho_r^0}{a^4}.
\end{eqnarray}
Here superscript $0$ denotes the density today. However, instead of $\rho_\chi$ the gravitating energy density is now the density $\rho_X =
\gamma_\chi \rho_\chi$ from definition Eq.(\ref{x-comp}), as implied by Eq.(\ref{friedmann}).

The equations for the perturbed metric are
\begin{eqnarray} \label{emetric1}
k^2\eta - \frac{1}{2}H\dot{h} =
\frac{a^2}{2\kappa^2}\delta T^0_0,
\end{eqnarray}
\begin{eqnarray}
k^2\dot{\eta}=\frac{a^2}{2\kappa^2}ik_i\delta T^0_i,
\end{eqnarray}
\begin{eqnarray} \label{emetric3}
\ddot{h}+2H\dot{h}-2k^2\eta=-\frac{a^2}{\kappa^2}\delta T^i_i,
\end{eqnarray}
\begin{eqnarray}
\ddot{h}+6\ddot{\eta}+2H(h'+6\dot{\eta})-2k^2\eta=\frac{3a^2}{\kappa^2}(\hat{k}_i\hat{k}_j-\frac{1}{3}\delta_{ij})\Sigma^i_j,
\end{eqnarray}
where the components of the perturbed stress energy tensor are
\begin{eqnarray}
\delta T^0_0 = -\rho_r\delta_r- \rho_\chi(\gamma_\chi'\varphi+\gamma_\chi\delta_\chi) -
   \rho_b \delta_b  -
   \rho_c \delta_c  - \frac{1}{a^2}\dot{\phi}\dot{\varphi} - V'\varphi,
\end{eqnarray}
\begin{eqnarray}
ik_i\delta T^0_i=\frac{4}{3}\rho_r\delta_r\theta_r+
\gamma_\chi \rho_\chi\theta_\chi +
\rho_b\theta_b +
\dot{\phi}k^2\dot{\varphi},
\end{eqnarray}
\begin{eqnarray}
\delta T^i_i = \rho_r\delta_r + 3c_b^2\rho_b\delta_b + \frac{3}{a^2}\dot{\phi}\dot{\varphi}
       - 3 V'\varphi.
\end{eqnarray}
We have grouped together photons and
neutrinos with subscript $r$, since their contribution is as usual, and used $\varphi$ to denote $\delta \phi/\phi$ as in\cite{Ferreira:1997hj}.
In addition to the field equations, we need the equations of motion for the individual components. For the perturbations of the coupled scalar field,
we derive the Klein-Gordon equation from Eq.(\ref{eom}) to find
\begin{eqnarray} \label{klein}
\ddot{\varphi} + 2H\dot{\varphi} + (a^2 V'' + k^2)\varphi + \frac{1}{2}\dot{\phi}\dot{h} =
-a^2\rho_\chi(\gamma_\chi'\delta_\chi+\gamma_\chi''\varphi).
\end{eqnarray}
For the $\chi$-component, the Bianchi identities Eq.(\ref{bianchic}) in the linear order are
\begin{eqnarray}
\dot{\delta}_\chi = -\theta_\chi - \frac{1}{2}\dot{h},
\end{eqnarray}
\begin{eqnarray} \label{vel}
\dot{\theta}_\chi = -H\theta_\chi + \frac{\gamma_\chi'}{\gamma_\chi}(k^2\varphi - \dot{\phi}\theta_\chi).
\end{eqnarray}
Conservation equations for uncoupled matter stay unmodified from the ones given in\cite{Ma:1995ey}.

\section{Model with two cold dark matter species}

\subsection{Background solution}

In this section we investigate the model proposed by Huey and Wandelt\cite{Huey:2004qv}. In this model quintessence with an exponential potential,
\begin{eqnarray}
V(\phi) = V_0 e^{-\kappa\alpha\phi},
\end{eqnarray}
is exponentially coupled to $\chi$-matter
\begin{eqnarray} \label{coupling}
\gamma_\chi(\phi) = e^{\kappa\beta(\phi-\phi_c)}.
\end{eqnarray}
There is also present an uncoupled species of cold DM. At early times, the field behaves as standard exponential
quintessence, but when it reaches the minimum of its effective potential, $V_{eff} = V + \gamma_\chi\rho_\chi$, it evolves to a
potential-dominated stage driving the acceleration of the universe.

There is motivation for the additional complexity of introducing two kinds of DM. It is well known that with minimally coupled exponential
quintessence the tracking solutions do not yield an accelerating phase\cite{Copeland:1997et}. If the field is exponentially coupled to matter, there
exists an accelerating attractor\cite{Amendola:1999er}, but obviously the field could not have reached it until today lest there would not have been
a matter dominated era at all. Moreover, it is known that in the such models the coupling between DE and DM is tightly constrained by the CMB
spectrum\cite{Amendola:2002bs} and other cosmological data\cite{Franca:2003zg}.

The amount of quintessence during BBN must be small, constraining $\alpha \gtrsim 5$ \cite{Copeland:1997et}. The onset of acceleration should occur
after matter-radiation equality, which is achieved when $\kappa\phi_c > 108/\alpha$. Finally, consistent late-time background evolution requires
$\alpha/\beta \lesssim 3/5$ \cite{Huey:2004qv}. As a representative parameter combination we will use $\alpha=5$, $\beta=15$, $\phi_c=25$ in numerical
calculations. Fig.(\ref{omegas_i}) shows then the evolution of the fractional energy densities
$\Omega_i \equiv \kappa^2 \rho_i/(3H^2)$. We have arranged the interacting and standard CDM
components to be of equal importance today. We see some transient oscillations at the late epoch when the coupling term begins
to hold the field at the minimum of its effective potential. However, asymptotically the coupling will keep the ratio of quintessence and interacting
DM densities constant and the field evolution is again characterized with a constant scaling.

Consider the component $\rho_X \equiv \gamma_\chi\rho_\chi$. Since during the tracking phase, assuming a constant background equation of state $w_B$,
\begin{eqnarray} \label{tracker}
\kappa\phi = \frac{3(1+w_B)}{\alpha}\log(a) + constant,
\end{eqnarray}
then $\rho_X \sim a^{3[-1+\frac{\beta}{\alpha}(1+w_B)]}$. Thus this energy density is growing in a phantom-like manner. Its effective equation-of
state parameter, defined by
\begin{eqnarray} \label{wxeff}
\dot{\rho}_X + 3H\rho_X(1+w_X^{(eff)}) = 0,
\end{eqnarray}
is shown together with the total equation of state of the universe in the left panel of Fig.(\ref{eos_i}). Similarly we
define the effective equation of state for the field $\phi$:
\begin{eqnarray} \label{wpeff1}
\dot{\rho}_\phi + 3H\rho_\phi(1+w_\phi^{(eff)}) = 0.
\end{eqnarray}
Then we have from Eq.(\ref{eom2}) that
\begin{eqnarray} \label{wpeff}
\dot{\rho}_\phi + 3H(\rho_\phi+p_\phi) = -\gamma_\chi'(\phi)\rho_\chi\dot{\phi} \quad \Rightarrow \quad
       w_\phi^{(eff)} = \frac{p_\phi+\gamma_\chi'\rho_\chi\dot{\phi}/(3H)}{\rho_\phi}.
\end{eqnarray}
We plot both $w_\phi$ and $w_\phi^{(eff)}$ in the right panel of Fig.(\ref{eos_i}).

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\textwidth]{omegas_i.eps}
\caption{\label{omegas_i}Evolution of the fractional energy densities in model of section III. The solid line is $\Omega_\phi$, the dashed line
$\Omega_X$, the dotted line is $\Omega_r$ and the dash-dotted line $(\Omega_c+\Omega_b)$.}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\textwidth]{wb_i.eps}
\includegraphics[width=0.45\textwidth]{wa_i.eps}
\caption{\label{eos_i}Left panel: Total equation of state $w$ (solid line) and the effective $w_X^{(eff)}$ (dashed line) for interacting CDM in the
model of section III. Since $w<-1/3$ today, the universe accelerates. Right panel: Equation of state for the quintessence in the same model.
Solid line is the formal $w_\phi$, and dashed line is the effective $w_\phi^{(eff)}$.}
\end{center}
\end{figure}

\subsection{Perturbation evolution}

Defining $C \equiv \log(\gamma_\chi)$, the coupled perturbation equations for the component $X$ can be written as\cite{Amendola:2003wa}
\begin{eqnarray} \label{edelta}
\dot{\delta}_X = -\theta_X - \frac{1}{2}\dot{h} + C'\dot{\varphi}+C''\dot{\phi}\varphi,
\end{eqnarray}
\begin{eqnarray} \label{etheta}
\dot{\theta}_X = -H\theta_X + C'(k^2\varphi - \dot{\phi}\theta_X).
\end{eqnarray}
For the largest scales the source term in Eq.(\ref{etheta}) can be neglected, and thus no velocity perturbations are generated. Since then
$\dot{\delta_c}-\dot{\delta}_X = C'\dot{\varphi}$, the coupling has a small effect on $\delta_X$, which then follows closely the standard CDM
overdensities.

To find the small scale evolution of perturbations, we follow
derivations found in Refs.\cite{Amendola:1999er,Amendola:2001rc,
Amendola:2002mp,Amendola:2003wa}. Using a linear combination of Eqs.(\ref{emetric1}) and (\ref{emetric3}),
\begin{eqnarray}
\ddot{h} + H\dot{h} = \frac{a^2}{\kappa^2}\left[\delta T^0_0-\delta T^i_i\right],
\end{eqnarray}
and averaging over the oscillating time derivatives $\ddot{\varphi}$, $\dot{\varphi}$ and $\delta_r$, one can combine Eqs. (\ref{edelta}) and
(\ref{etheta})
into
\begin{eqnarray} \label{edelta2}
\ddot{\delta} + H\dot{\delta} - \frac{a^2}{2\kappa^2} \rho_X \delta_X - C'\dot{\phi}\theta = [-C'k^2 + HC''\dot{\phi} + \ddot{C'} -
                                \frac{a^2}{\kappa^2}V']\varphi
                              + \frac{a^2}{2\kappa^2}(\rho_c\delta_c+\rho_b\delta_b),
\end{eqnarray}
when $c_b^2 \approx 0$. Averaging out the small and oscillatory $\ddot{\varphi}$ and $\dot{\varphi}$ also from Eq.(\ref{klein}) yields
\begin{eqnarray} \label{phiper}
\varphi = -\frac{a^2\rho_X C'\delta_X + \frac{1}{2}\dot{\phi}\dot{h}}{a^2(V'' + \rho_X C'') + k^2}.
\end{eqnarray}
This approximation is in fact reasonably good for all scales. We have tested it by comparing the LHS and RHS of this expression
evaluated by numerically integrating the full perturbation equations\footnote{In numerical calculations we use the public
CAMB code\cite{Lewis:1999bs}, see http://camb.info/. For simplicity, we assume scale-invariant initial power spectrum, no reionization and three
massless neutrino species. In our calculations, $h=0.71$. Normalization is such that the primordial curvature perturbation equals unity.}. Inserting
the approximation in Eq.(\ref{edelta2}) and using Eq.(\ref{etheta}),
we get in the small scale limit
\begin{eqnarray} \label{edelta3}
\ddot{\delta}_X + \left(H+C'\dot{\phi}\right)\dot{\delta}_X = \frac{3}{2}H^2\left[\Omega_X\left(1+2\frac{C'^2}{\kappa^2}\right)\delta_X +
\Omega_c\delta_c + \Omega_b\delta_b\right].
\end{eqnarray}
Here we have used $C''=0$. During tracking era, $\Omega_X \sim a^{3[(1+w_B)(\frac{\beta}{\alpha}+1)-1]}$ vanishes to a good approximation.
If we assume that then the noninteracting matter perturbation scales as $\delta_c \sim \tau^{m-2}$, we can use the tracker solution Eq.(\ref{tracker})
to find that
\begin{eqnarray} \label{edelta4}
\ddot{\delta}_X + \left[1+\frac{3\beta}{\alpha}(1+w_B)\right]\frac{2}{(1+3w_B)\tau}\dot{\delta}_X = A\tau^m,
\end{eqnarray}
with the constant $A$ determined by the magnitude of noninteracting matter perturbations at a given time. The full solution to this equation is
\begin{eqnarray}
\delta_X = D + B\tau^{1-b} + \frac{A}{(b+m+1)(m+2)}\tau^{m+2},
\end{eqnarray}
where $B$ and $D$ are integration constants and $b=[2+6\beta(1+w_B)/\alpha]/(1+3w_B) \gg 1$. Thus the last term gives the dominant mode, which has the
same scaling as the noninteracting DM. Therefore the ratio $\delta_X/\delta_c$ is constant during tracking era.
During matter domination, when $m=2$, this means that $\delta_X \sim a$, and $\delta_X/\delta_c = 3(1-3/\alpha^2)/(10+12\beta/\alpha)
\ll 1$.

When the field reaches the minimum of its effective potential, it evolves with the rate\cite{Huey:2004qv}
\begin{eqnarray} \label{trans1}
\kappa\dot{\phi} = \frac{3}{\alpha+\beta}H.
\end{eqnarray}
The critical period we are interested in is the transition to the joint domination of quintessence and interacting matter that is ongoing today. The
field derivative is then oscillating about the value given by Eq.(\ref{trans1}), to which it will asymptotically settle (see Fig.(\ref{eos_i})). Since
$\Omega_X$ is now approaching $\Omega_c$, and $(1+C'^{2}) \gg 1$, we approximate Eq.(\ref{edelta3}) by dropping the source terms due to noninteracting
matter. This approximation is well justified since, as it turns out, the RHS of Eq.(\ref{edelta3}) is soon dominated by the rapidly growing
perturbation in the density of interacting DM.
We therefore write
\begin{eqnarray} \label{edelta10}
\ddot{\delta}_X + \left(1+\frac{3\beta}{\alpha+\beta}\right)H\dot{\delta}_X = \frac{3}{2}H^2\Omega_X\left(1+2\beta^2\right)\delta_X.
\end{eqnarray}
To solve this equation analytically, we would need expressions for the background quantities $H$ (which follows from $w_B$) and $\Omega_X$. To that
end we use the asymptotic value also for the latter
\begin{eqnarray} \label{trans2}
w_B=-\beta/(\alpha+\beta), \quad \Omega_X = \alpha/(\alpha+\beta).
\end{eqnarray}
Inserting these in Eq.(\ref{edelta10}) yields the solutions
\begin{eqnarray}
\delta \sim a^n, \quad n= \frac{1}{4}\frac{(\alpha+10\beta)}{(\alpha+\beta)}
                 \left[-1 \pm \sqrt{1 + \frac{24\alpha(\alpha+\beta)(1+2\beta^2)}{(\alpha+10\beta)^2}}\right].
\end{eqnarray}
The exponent of the growing solution (corresponding to the positive sign) is large for typical values in this model. For $\alpha=5$ and $\beta=15$, $n
\approx
11.2$. This is in strong contrast to standard DM perturbations growth rate of which is slowing after the matter domination when $\delta_c \sim a$.
Therefore
\begin{eqnarray}
\theta_X \sim \dot{\delta}_c - \dot{\delta}_X \sim a^r, \quad r = n - \frac{2\beta-3\alpha}{2(\alpha+\beta)},
\end{eqnarray}
which is, consistently, the growing solution of Eq.(\ref{etheta}) in this limit. Numerical results are shown in Fig.(\ref{deltas_i})\footnote{Since
we have normalized the primordial curvature perturbation to unity, these perturbations in fact exit the linear regime at about $\delta \sim 10^5$.
So these calculations are untrustworthy beyond those values, but that is unrelevant to our conclusions.}.
There we see that the interacting DM density contrast adapts to this asymptotic scaling in fact as the transition to acceleration begins,
although the solution Eqs.(\ref{trans1}),(\ref{trans2}) has not been reached.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\textwidth]{pert_a.eps}
\caption{\label{deltas_i} Interacting DM overdensities in the model of section III. The slope $s$ of the curves in the logarithmic plot is
$s \approx 2$, $1$, $11.2$ early in the radiation domination (when the scale is outside the horizon), during matter domination and during the
transition to accelerating universe, respectively. The $k$-values from bottom to top are $k = 2.4 \cdot 10^{-6}$, $2.4 \cdot 10^{-5}$, $2.4
\cdot 10^{-4}$, $0.0024$,
$0.024$ and $0.24$ Mpc$^{-1}$.}
\end{center}
\end{figure}

We conclude that when the energy in the $\chi$-matter is becoming a significant contributor to the background expansion, the perturbation
growth in this component is almost explosively sped up by the interaction pumping energy into it from the $\phi$-field.
As seen from Eq.(\ref{phiper}), the DE is then inhomogenenous on small scales. It has been found also that in the nonlinear
regime DE tends to clump with DM if coupled\cite{Mota:2004pa,Nunes:2004wn,vandeBruck:2005ii}. The large coupling
for which $C'=\beta$ in this model results in a large effective gravitational constant in Eq.(\ref{edelta10}), $G^{eff} = (1+2\beta^2)G$. In earlier
cosmology this is not as important, since then the standard DM overdensities constitute the dominant gravitational sources. There the modified Hubble
friction term in Eq.(\ref{edelta3}) acts to reduce the relative magnitude of $\delta_X$ to $\delta_c$, but these evolve with the same rate.
However, in the late universe the cosmic structure is drastically increased, except at the largest scales where we see only little oscillations.
Consequently, the shape of the matter power spectrum in this model is highly incompatible with observations. Also, as the increase in structure will
cause rapid deepening of the gravitational wells, the resulting CMB spectrum is modified by a strong late integrated Sachs-Wolfe effect due to time
variation of the gravitational potentials.
We have confirmed these considerations by numerical integration for several parameter values satisfying the relations given in the previous
subsection. As a non-negligible amount of $\chi$-matter and a relatively strong coupling are required in this model, we feel it safe to state
although having not performed an extensive exploration in the space of all cosmological parameters, that this model cannot be succesfully confronted
with observations.

\section{Model with polynomial coupling}

\subsection{Background solution}

The model proposed by Bean and Magueijo\cite{Bean:2000zm} is another example of a modified exponential quintessence scenario. Again a
field is coupled to DM in such a way that quintessence is dominant today and driving the acceleration of the universe while the model
still has its parameters of the order of the Planck scale and its outcome widely independent of the initial conditions for the field. This is achieved
with
only one DM species by using a non-exponential form for the coupling. To
be definite, we have in the action Eq.(\ref{action})
\begin{eqnarray}
V(\phi) = V_0 e^{-\kappa\alpha\phi},
\quad
\gamma_\chi(\phi) = 1 + \lambda[\kappa(\phi-\phi_0)]^b.
\end{eqnarray}
For numerical values we will use $\alpha = 8$, $b=8$, $\lambda=50$ and $\kappa\phi_0=32.5$.
The background evolution is shown is Fig.(\ref{omegas_d}).
In this model the field leaves the standard exponential track long before matter domination. After initial transients, the field
tracks the background radiation, until the coupling term pushes the field into kination. This lasts until the field reaches the minimum of its
effective potential. Then it will at due time drive the acceleration. However, as the matter density eventually dilutes, the coupling force will
fade, leading the field back to standard scaling in the asymptotic future. Thus matter domination is restored and the acceleration in this model
is transient. We plot the effective equation of state parameter for the field $\phi$, as defined in Eq.(\ref{wpeff}), in the left panel of
Fig.(\ref{eos}). In the right panel we plot the total equation of state for the universe together with the $w_X^{(eff)}$ as defined in
Eq.(\ref{wxeff}). Since in this model $\rho_X$ governs the background expansion also in the matter dominated era, it is important that the coupling
term has then negligible effect on the scaling of this density, since a significant deviation from $a \sim \tau^2$ would result in modified conformal
distance to the last scattering surface, possibly dangerous to the compatibility with observations of the peaks in the fluctuation spectrum of the
CMB radiation\cite{Hoffman:2003ru}. One also expects that then the growth rate of DM perturbations will not be much modified.
However, one would guess that the nonstandard evolution during transition to DE domination, seen in Figs.(\ref{omegas_d}) and (\ref{eos}), has
some effects on the perturbation growth as was the case in the model of section III. Indeed these effects prove fatal to this model, as will be
seen below.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\textwidth]{omegas_d.eps}
\caption{\label{omegas_d}Evolution of the fractional energy densities in the model of section IV. The solid line is $\Omega_\phi$, the dashed line
$\Omega_X$. Dotted line is $\Omega_r$ and the dash-dotted line $\Omega_b$.}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\textwidth]{wa_d.eps}
\includegraphics[width=0.45\textwidth]{wb_d.eps}
\caption{\label{eos}Left panel: Total equation of state $w$ (solid line) and the effective $w_X^{(eff)}$ (dashed line) for interacting DM in the
model of section IV. Since $w<-1/3$ today, the universe accelerates. Right panel: Equation of state for the quintessence for the same model. Solid
line is the formal $w_\phi$, and dashed line is the effective $w_\phi^{(eff)}$.}
\end{center}
\end{figure}

\subsection{Perturbation evolution}

The linearized Einstein equations have in fact been solved in this model\cite{Bean:2001ys}. However, this was not done taking fully into account
the impact of the coupling to the matter perturbations, but instead by assuming that the fluctuations in $\rho_\chi$ decouple from those in
$\phi$. This was realised by setting the DM velocity perturbation to zero, as conventional in the synchronous gauge. However, now the interaction
with DE will drive $\theta_\chi$ to evolve even if its initial value is chosen to be zero. One sees that the source term in the Euler
equation Eq.(\ref{vel}) vanishes only in the absence of coupling or if the DE is perfectly smooth. Neither is the case now. We show the
effect of physical assumptions in Fig.(\ref{spek}).

Since now $C''=0$, Eq.(\ref{edelta3}) is not valid. However, using the approximations that lead to that equation, we can derive the corresponding
evolution equation for the quantity $\delta_\chi$. It should capture the qualitative behaviour of the DM perturbation, since $\delta_X=
\delta_\chi +C'\varphi \approx \delta_\chi$ for small scales. The equation we find reads
\begin{eqnarray} \label{edelta5}
\ddot{\delta}_\chi + \left(H-\frac{\lambda b y^{b-1}}{1+\lambda y^b}\kappa\dot{\phi}\right)\dot{\delta}_\chi =
                \frac{3}{2}H^2\Omega_X\left[1+\frac{\lambda y^b(\lambda y^{b-2}(2b^2-y^2)-1)}{(1+\lambda y^b)^2}\right]\delta_\chi,
\end{eqnarray}
where $y \equiv \kappa(\phi-\phi_0)$. The effective gravitational constant $G_\chi^{eff}$ can be thought to be the
expression is square brackets times $G$. We plot $G^{(eff)}/G-1$ as a function of $\phi$ in Fig.(\ref{coup}) for a choice of parameters.
The values of $G^{eff}$ becomes relevant at the matter dominated era, when the source term in the
RHS of Eq.(\ref{edelta5}) is non-negligible. However, as the coupling has driven $\phi$ near to $\phi_0$, we have then $G_\chi^{eff} \approx G$
(for our example parameters, $-0.5<y<0$ from $a = 10^{-4}$ until $a = 0.1$). This changes when $\Omega_\phi$ climbs up, since then $\phi$ rolls
forward. Similarly as in the previous case, $\delta_X$ is driven to rapid increase. We show its evolution in Fig.(\ref{deltas_d}), where we also
plot the baryon overdensities $\delta_b$ for comparison. The boost experienced by $\delta_X$ is not as vast as we saw in the previous section, but still
results in an order of magnitude or two too large $\delta_X$. Again we believe that notable improvement is not found by adjustments of parameters, but
by revision of the scenario.

\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\textwidth]{dilspek.eps}
\caption{\label{spek} The CMB spectrum in the model of section IV (solid line). Dash-dotted line corresponds to suppressing the coupling of dark
energy and DM perturbations (i.e. $\theta_\chi=0$), and dashed line corresponds to suppressing DE perturbations (i.e. $\varphi=0$).}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.45\textwidth]{coup.eps}
\caption{\label{coup} The deviation of the effective gravitational constant from the standard one, $G^{(eff)}/G-1$, as a function of the field
$\kappa\phi$ for the model of section IV. The solid curve corresponds to the $G_\chi^{(eff)}$ in Eq.(\ref{edelta5}), and the dashed curve is $2C'^2$,
corresponding to $G^{eff}_X$ as it appears in Eq.(\ref{edelta3}). For both definitions the deviation is small when $\phi \approx \phi_0$, but becomes
very rapidly large when the field $\phi$ evolves to larger values.}
\end{center}
\end{figure}
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.7\textwidth]{pert_b.eps}
\caption{\label{deltas_d} DM overdensities (solid curves) in the model of section IV. Dashed curves are $\delta_b$. The $k$-values from
bottom to top are $k = 2.4 \cdot 10^{-6}$, $2.4 \cdot 10^{-5}$, $2.4 \cdot
10^{-4}$, $0.0024$, $0.024$ and $0.24$ Mpc$^{-1}$.}
\end{center}
\end{figure}

Finally, a remark about the adiabatic initial conditions we have used in the calculations. Adiabaticity of perturbations\cite{Liddle:2000cg}
means that given any two superhorizon regions $A$ and $B$ in a perturbed universe at an instant $\tau$, $B$ is identical to $A$ at some other instant
$\tau + \delta \tau$. Evolution of the regions is the same, but slightly asynchronous. Then the ratio of fluctuation and
time derivative of say a density field is common to all density fields. Thus we can define the entropy between species
$i$ and $j$ as
\begin{eqnarray} \label{entropy}
S_{ij} \equiv \frac{\delta \rho_i}{\dot{\rho_i}} - \frac{\delta \rho_j}{\dot{\rho_j}}
         =    \frac{\delta_i}{1+w_i^{(eff)}} - \frac{\delta_j}{1+w_j^{(eff)}}.
\end{eqnarray}
The general adiabatic condition then dictates that all $S_{ij}$'s together with their derivatives vanish. Note that only in the absence of
interactions does this condition coincide with the usually cited
\begin{eqnarray} \label{entropy2}
\frac{\delta_i}{1+w_i} = \frac{\delta_j}{1+w_j}, \quad \theta_i = \theta_j.
\end{eqnarray}
There can be difference between these conditions, as seen for the cases we are now considering in Figs.(\ref{eos_i}) and (\ref{eos}). For a scale far
outside the horizon and deep in the radiation dominated era, the growing adiabatic mode\cite{Ma:1995ey, Bucher:1999re} of the scalar field
perturbation satisfies
\begin{eqnarray}
\varphi = \frac{3\phi^2-(\frac{1}{2}V'-\frac{1}{6}\gamma_\chi'\rho\chi)\dot{\phi} \tau
          +\frac{1}{2}\rho_\chi\left[\gamma_\chi''\dot{\phi}^2 - \gamma_\chi'a^2V'-\gamma_\chi'^2a^2\rho_\chi\right]\tau^2}
          {(6\dot{\phi}+\gamma_\chi'a^2\rho_\chi \tau)V' - \gamma_\chi''\rho_\chi \dot{\phi}^2\tau} \dot{\phi}Ak^2\tau^2,
\end{eqnarray}
\begin{eqnarray}
\dot{\varphi} =  \frac{(\frac{4}{3}\gamma_\chi'\rho_\chi a^2 V'+\frac{1}{2}a^2V'^2 -\frac{1}{2}\gamma_\chi''\rho_\chi\dot{\phi}^2)\tau
               + a^2\rho_\chi\left[-\frac{1}{2}\gamma_\chi''(V'+\frac{1}{3}\gamma_\chi'\rho_\chi) + \frac{1}{2}\gamma' a^2 V' +
                 \frac{4}{3} \gamma_\chi'^2 a^2\rho_\chi V'\right]\tau^2}
          {(6\dot{\phi}+\gamma_\chi'a^2\rho_\chi \tau)V' - \gamma_\chi''\rho_\chi \dot{\phi}^2\tau} \dot{\phi}Ak^2\tau^2.
\end{eqnarray}
Normalization $A=-1/2$ is convenient and sets comoving curvature perturbation equal to unity. Fortunately the above expressions can in many
occasions be simplified by dropping the square bracket terms, but we have kept them here for the sake of completeness.
The departure of the usual adiabatic condition Eq.(\ref{entropy2}) from
the generalized one has been pointed out also in Refs.\cite{Malik:2002jb,Malik:2004tf}.
If the
field is a tracker, the initial conditions may indeed be irrelevant also for the perturbed field. However, for minimally coupled fields it has been
shown that in some instances this is not the case\cite{Kawasaki:2001nx,Abramo:2001mv}, while isocurvature perturbations in
coupled quintessence remain to be systematically studied.

\section{Discussion}

Interestingly, in the two models we have investigated, the growth of DM perturbations is enchanced, whereas in minimally coupled models
the late time effect of DE is the opposite. This may be understood by comparing to the case where the interacting DE and DM satisfy the adiabatic
relation $S_{\phi \chi}=\dot{S}_{\phi \chi}=0$, where $S_{\phi \chi}$ is defined by Eq.(\ref{entropy}). Then the system of these components
can be treated as a unified fluid without intrinsic entropy. It is known that the effective sound speed squared $c_S^2 \equiv \dot{p}/\dot{\rho}$ of
such a fluid governs the late dynamics of the perturbations\cite{Reis:2005wz, Koivisto:2004ne}. If $c_S^2>0$, they are driven to oscillate, if
$c_S^2<0$ they tend to blow up. This is the work of the pressure gradient sourcing the evolution equation one can derive for the unified fluid
density contrast,
\begin{eqnarray} \label{udeltae}
\ddot{\delta}+[1-3(2w-c_S^2)]H\dot{\delta}-\frac{3}{2}(1-6c_S^2+8w-3w^2)H^2\delta = -k^2 \frac{\delta p}{\delta \rho} \delta.
\end{eqnarray}
This equation is exact (to linear order, in the comoving gauge). As $w$ and $c_S^2$ are given by the background expansion, one needs only information
of the pressure perturbation to solve the structure in the universe. In the adiabatic case, $\delta p/\delta \rho = c_S^2$, but in the scalar
field models considered here this assumption is not valid. However, using equations from subsection IIB, the small scale limit of the pressure
gradient in the late universe is readily found. It is
\begin{eqnarray} \label{gradient}
-k^2\frac{\delta p}{\delta \rho} = -k^2\frac{\frac{1}{a^2}\dot{\phi}\dot{\varphi}-V'(\phi)\varphi}{\rho_\chi\delta_\chi -2 V'(\phi)\varphi}
                                 \rightarrow -a^2 C'(\phi) V'(\phi),
\end{eqnarray}
(also in the comoving gauge) and turns out positive for the models of section III and IV. Thus one may regard the enchanced small scale growth rate
there as a consequence of negative effective (non-adiabatic) sound speed squared. Now the pressure gradient approaches a $k$-independent expression and the
growth rate saturates at a given value when $k$ is increased beyond some critical scale, unlike in the adiabatic case. Note also that the total
density perturbation $\delta$ in Eq.(\ref{udeltae}),
\begin{eqnarray}
\delta = \frac{\rho_\chi \gamma'_\chi(\phi)\delta_\chi + [\rho_\chi \gamma'(\phi) + V'(\phi)]\varphi + \frac{1}{a^2}\dot{\phi}\dot{\varphi}}
              {\gamma_\chi(\phi)\rho_\chi + \frac{1}{a^2}\dot{\phi}^2 + V(\phi)},
\end{eqnarray}
is directly relevant to the integrated Sachs-Wolfe effect in the CMB fluctuation spectrum.

Before concluding, we use the opportunity to comment on yet another model with DE-DM interaction\cite{Chimento:2003ie}. There DE with a constant
equation of state parameter $w_\phi$ is coupled to DM in such a way that
\begin{eqnarray} \label{cont1}
\dot{\rho}_\phi + 3H\rho_\phi = 3H \lambda^2 (\rho_X + \rho_\phi),
\end{eqnarray}
\begin{eqnarray} \label{cont2}
\dot{\rho}_X + 3H\rho_X = -3H \lambda^2 (\rho_X + \rho_\phi),
\end{eqnarray}
where $\lambda^2$ is a constant measuring the intensity of the interaction. It might be difficult to find a field theory underlying this
phenomenological model, but that would be necessary to be able to derive the corresponding equations to the linear order. Otherwise they must be put
in by hand.
The linear DE continuity equations presented in the recent paper\cite{Olivares:2005tb} imply that there
\begin{eqnarray} \label{div1}
\nabla_\mu {T^\mu_0}^{(\phi)} = 3H\rho_\phi \lambda^2(\delta_\phi + r\delta_X),
\end{eqnarray}
\begin{eqnarray} \label{div2}
\nabla_\mu {T^\mu_i}^{(\phi)} = [3H\rho_\phi \lambda^2(1+r)\theta_\phi]_{,i},
\end{eqnarray}
where $r \equiv \rho_\chi/\rho_\phi$. Except perhaps for the sign of the $0$-component of the divergence\footnote{The sign is different from the
zero-order divergence. Possibly this is a misprint.}, these expressions are not unreasonable, but do not follow unambiguously from Eqs.(\ref{cont1})
and (\ref{cont2}). However, once the divergence of the DE stress tensor is given, the interacting DM
continuity equations are uniquely fixed. When Eqs.(\ref{div1}) and (\ref{div2}) hold for the DE and the DM Lagrangian is effectively
of the form (\ref{lagran}), the Bianchi identities determine that
\begin{eqnarray}
\dot{\delta}_X=-\theta_X-\frac{1}{2}\dot{h}-3H\lambda^2(\frac{1}{r}\delta_\phi+\delta_X),
\end{eqnarray}
\begin{eqnarray} \label{joku}
\dot{\theta}_X=-H\theta_X+3H\lambda^2(1+\frac{1}{r})\theta_\phi.
\end{eqnarray}
From these we recover the equations used in Ref.\cite{Olivares:2005tb} only by setting $\theta=0$ in the first equation and forgetting about the
second one. But as detailed in the previous section, such approximation can leave crucial features out from the evolution of perturbations. Therefore
we must regard that the results of the data analysis in Ref.\cite{Olivares:2005tb}, where it is announced that observations prefer interacting DE
models, call for reinvestigation.

As mentioned in the beginning of this paper, the origin of most of the energy density in the universe is unknown. Suggestions can be
based on speculations of string theory, but this is tentative at the present. However, some inventive mechanism, as the ones considered here, is
necessary if some light is required to be shed on the coincidence problem. Moreover, as the results of this paper demonstrate, considerations of
cosmological structure provide powerful means to constrain such mechanisms.

\acknowledgments{The author acknowledges useful discussions with Hannu Kurki-Suonio, David Mota and Finn Ravndal. This work was supported in part by
NorFA, Waldemar von Frenckels Stiftelse and Emil Aaltosen S\"a\"ati\"o.

redpajama_set_name: RedPajamaArXiv


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The corneal crosslinking process involves dropping Vitamin B2 into the patient's eye and exposing the cornea to UV rays. Before the procedure the patient will be given local anaesthetic drops, so the procedure will be painless. The combination of B2 and UV rays forms a chemical reaction that hardens the cornea. To prevent the keratoconus from progressing, the UV light encourages bonds between collagen fibrils to form which strengthens the cornea. To help with the healing process and to make the eye more comfortable, a contact lens will be placed on the patient's eye after the treatment.
Although this treatment will not restore the cornea back to its original rounded shape, this process has been proven to halt the progression of keratoconus in 94% of patients.
Intacs are very small clear plastic arcs that are designed to be inserted into the substance of the cornea. When they are inserted into the eye, intacs reshape the cornea by flattening it closer to its original dome shape. By flattening the steep part of the cornea or cone to reduce distortions helps to refocus light rays and improve vision. Although the procedure usually improves uncorrected vision, most patient who have had this procedure will still need glasses or contact lenses after the intacs are inserted.
When keratoconus continues to progress and contact lenses or intacs are no longer a solution, eye care professionals may recommend a corneal transplant. A corneal transplant operation involves replacing the damaged cornea with healthy donor tissue (human tissue provided by the National Eye Bank after careful quality screening). Depending on the severity of keratoconus, a corneal transplant may involve replacing one or more layers of the cornea. The entire cornea may be replaced if the keratoconus is severe.
If you are having difficulty with your vision and suspect you or your loved one may have keratoconus, we recommend you book an appointment at Auckland Eye. Here at Auckland Eye, we have most advanced technology and equipment to treat keretoconus and accurately determine the topography (shape and thickness) of the cornea, which allows us to screen for potential keratoconic changes to the eye. We offer the highest quality of care as each ophthalmologist has international and specialist training in specific eye diseases and surgery techniques to provide the best possible visual outcomes for all of our patients.


Stardom "Stardom X Stardom 2014"
Let's get to the Joshi goodness.
This match is for the Artist of Stardom Championship. Wakizawa and company attack their opponents before the match starts, Kuragaki stays in the ring with Iwatani and Iwatani hits a tilt-a-whirl headscissors. Dropkick by Iwatani, she picks up Kuragaki but Kuragaki picks her up and hits a military press slam. Yoneyama comes in the ring to kick Wakizawa and Matsumoto, then she along with Kamen and Kuragaki hit running strikes in the corner. They start getting beaned with the brown balls, Wakizawa and Matsumoto come in the ring and they all apply camel clutches while rubbing the brown fuzzy balls onto their opponents. Iwatani and Kuragaki stay in the ring, Iwatani ties up Kuragaki in the ropes as her teammates put a ribbon around her neck and pull in different directions. Yoneyama and Kamen come in the ring to break it up, and Kuragaki stomps on Iwatani back in the ring. Kuragaki picks up Iwatani and gets her onto her shoulders, but Iwatani slides off. Iwatani goes off the ropes and hits a sunset flip, but Yoneyama breaks it up. Kuragaki tags in Kamen, Kamen pushes Iwatani into the corner and hits repeated body shots. Irish whip by Kamen but Iwatani hits a rebound dropkick out of the corner and tags in Wakizawa. Lariat by Wakizawa to Kamen, she picks her up but Yoneyama runs in the ring. Wakizawa hits a DDT/neckbreaker combination on both of them, Wakizawa puts Kamen on the top turnbuckle while Matsumoto dumps a bunch of the brown balls in the ring, and Wakizawa hits a Frankensteiner. Matsumoto then goes up top while Iwatani holds Kamen, and Matsumoto hits a reverse splash. Iwatani now goes up top while Wakizawa holds down Kamen, and she hits a diving body press. Cover, but Kuragaki breaks it up.
This match is for the Goddesses of Stardom Championship. Takahashi and Kimura start things off. They jockey for position, Takahashi gets Kimura to the mat and goes for the arm, but Kimura rolls out of it and applies a front headlock. Side headlock takedown by Takahashi but Kimura gets out of it, trip and a cover by Takahashi but Kimura returns to her feet. Alpha Female comes in and attacks Takahashi from behind, and Kimura hits Hojo on the apron. Double Irish whip to Takahashi but she ducks the lariat and both wrestlers hit dropkicks as Hojo comes in the ring. Scoop slam by Takahashi, Hojo goes off the ropes and Takahashi catapults her so that Hojo can hit an elbow drop. Takahashi throws Kimura out of the ring, she goes off the ropes and goes for a tope suicida but Kimura hits her in the head with a steel chair. Alpha Female pulls Hojo out of the ring as all four wrestlers are on the floor, and Alpha Female throws Hojo into a row of chairs. Alpha Female attacks Hojo with a chair while Kimura takes Takahashi up into the crowd to slam her into a wall. Alpha Female and Kimura take their opponents back to ringside and throw them into each other on the floor. Kimura gets back in the ring with Takahashi, Kimura goes for a kick but Takahashi catches it. Lariat by Takahashi as Hojo runs in to hit Alpha Female, Takahashi picks up Kimura and holds her so that Hojo can hit a running elbow. Backdrop suplex by Takahashi, cover, but it gets a two count. Takahashi goes off the ropes but Kimura ducks the lariat, small package by Takahashi but it gets two. Kimura ducks Takahashi's kick but Takahashi gets out of the sleeper and delivers the kick anyway. Takahashi picks up Kimura but Kimura gets away and applies the sleeper. Hojo runs in and tries to break it up but Alpha Female cuts her off and stomps her onto the apron. Takahashi gets into the ropes to force a break, cover by Kimura but it gets a two count. Kimura picks up Takahashi but Takahashi slams Kimura to the mat. Kimura gets up in the corner and she drops Takahashi with a big boot, but Takahashi gets back up and hits a lariat. Another big boot by Kimura and they both knock their respective opponents off the apron. Elbows by Kimura and Takahashi, headbutt by Kimura and both wrestlers fall to the mat. Takahashi and Alpha Female are tagged in, dropkick by Hojo, Irish whip, reversed, and Alpha Female hits a lariat. Alpha Female picks up Hojo and throws her into the corner, Irish whip, but Hojo slides out to the apron.
This match is for the World of Stardom Championship. They circle each other to start, tie-up, Yoshiko pushes Shirai into the ropes and she gives a clean break. They lock up again, Shirai gets Yoshiko into the ropes but Yoshiko punches her. Yoshiko kicks Shirai down in the corner before flinging her to the mat by her hair. Facewashes by Yoshiko in the corner but Shirai catches her leg when she goes for a running kick and they trade strikes. Yoshiko pushes Shirai into the ropes and she gives a clean break. They lock knuckles, Yoshiko pushes Shirai to the mat and she goes for a backdrop suplex, but Shirai applies a side headlock and takes Yoshiko to the mat. Grounded facelock by Yoshiko but Shirai gets out of it, bodyscissors by Yoshiko and they both grab each other's hair while the referee tries to get them to stop. Cross armbreaker by Yoshiko but Shirai quickly gets to the ropes to force a break. Yoshiko wraps Shirai's arm in the top rope and kicks it, Yoshiko picks up Shirai and tries to Irish whip her but Shirai hangs onto the ropes. Irish whip by Yoshiko but Shirai ducks the lariat and hits a cartwheel dropkick. Yoshiko falls out of the ring, Shirai goes out to the apron but Yoshiko pulls her down to the floor. Kick to the head by Yoshiko and she slides Shirai back into the ring. Wristlock by Yoshiko and she applies the cobra twist, but Shirai rolls out of it and covers Yoshiko for a two count. Arm trap crossface by Shirai in the middle of the ring but Yoshiko muscles out of it, Yoshiko goes off the ropes but Shirai hits a drop toehold. She goes for a tiger feint kick but Yoshiko catches her leg and kicks Shirai in the face. Yoshiko then applies a choke on the apron before dumping Shirai down to the floor. Yoshiko stays on the apron and she hits a seated senton down onto a prone Shirai. Yoshiko picks up Shirai and puts her onto her shoulders, she walks up into the crowd but Shirai gets away and kicks Yoshiko in the head. Shirai climbs up on the entrance way and hits a moonsault on a standing Yoshiko. Shirai picks up Yoshiko and brings her back into the ring, Shirai gets on the apron and hits a swandive dropkick.
Best Match: Kyoko Kimura and Alpha Female vs. Nanae Takahashi and Kairi Hojo. It was a bit of a toss-up as I was more annoyed about this one being clipped, but it was still the best match on the card. All four wrestlers looked great, and it was a very clean win that really helped put over the new champions. I will talk about Hojo more below but she was great, and all the moves/transitions were hit crisply. The tag work was also really well done and the emotion was there so it felt like a title match. I wish more of it was shown but there is not much to complain about what did make it onto DVD.
MVP: Kairi Hojo. I already loved her anyway, as Hojo is just the right combination of cute and tough. But she was the star of the match, as in the end she was left alone with Alpha Female, out-striking the much larger gaijin and picking up the clean victory. Even before the ending she looked good though and was a constant presence in the match. She has been wrestling for less than three years and is only 26 years old, so hopefully she sticks to wrestling and continues to grow in the future.
Overall: I really wanted to love this event. All three title matches were good at what they were (the first isn't really my thing as I think the wrestlers are average, but it wasn't a total waste) and with so many title changes it felt like a big card. But the clippings on this events just hurts it for me, I am sure I would have enjoyed the last two matches more if I saw the entire thing, but clippings can really hurt the structure of the match. So the overall score is a bit higher than the scores may reflect as I think the action was really solid throughout, and if you don't mind clipped matches you'll probably like it even more than I did. With three title changes, there is a new wave coming to Stardom so it will be interesting to see how they do for the rest of the year.


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NYSE:EFX
Equifax - EFX Stock Forecast, Price & News
Adding Equifax Inc.
834,727 shs
Equifax MarketRank™ Forecast
5.1% Downside
3.78% of Shares Sold Short
Based on 9 Articles This Week
$15,958 Sold Last Quarter
117th out of 324 stocks
Consumer Credit Reporting Agencies, Mercantile Reporting Agencies, Industry
5th out of 6 stocks
Equifax has received a consensus rating of Hold. The company's average rating score is 2.44, and is based on 8 buy ratings, 7 hold ratings, and 1 sell rating.
According to analysts' consensus price target of $206.13, Equifax has a forecasted downside of 5.1% from its current price of $217.18.
Equifax has been the subject of 9 research reports in the past 90 days, demonstrating strong analyst interest in this stock.
3.78% of the outstanding shares of Equifax have been sold short.
Equifax has a short interest ratio ("days to cover") of 4.6.
Short interest in Equifax has recently increased by 1.31%, indicating that investor sentiment is decreasing.
Equifax has a dividend yield of 0.72%, which is in the bottom 25% of all stocks that pay dividends.
Equifax does not have a long track record of dividend growth.
The dividend payout ratio of Equifax is 27.08%. This payout ratio is at a healthy, sustainable level, below 75%.
Based on earnings estimates, Equifax will have a dividend payout ratio of 20.69% next year. This indicates that Equifax will be able to sustain or increase its dividend.
Equifax has received a 39.43% net impact score from Upright. The largest positive contribution comes from its "Distributing knowledge" impact, which is mostly driven by its "Credit reporting services", "HR management systems", and "Consumer data software" products. See details.
The Environmental Impact score for Equifax is -0.68.
Equifax has a news sentiment score of 0.34. This score is calculated as an average of sentiment of articles about the company over the last seven days and ranges from 2 (good news) to -2 (bad news). This is a lower news sentiment than the 0.59 average news sentiment score of Business Services companies.
MarketBeat has tracked 9 news articles for Equifax this week, compared to 8 articles on an average week.
Only 4 people have searched for EFX on MarketBeat in the last 30 days. This is a decrease of 0% compared to the previous 30 days.
In the past three months, Equifax insiders have sold more of their company's stock than they have bought. Specifically, they have bought $0.00 in company stock and sold $15,958.00 in company stock.
Only 1.57% of the stock of Equifax is held by insiders.
93.84% of the stock of Equifax is held by institutions. High institutional ownership can be a signal of strong market trust in this company.
Earnings for Equifax are expected to grow by 0.13% in the coming year, from $7.53 to $7.54 per share.
The P/E ratio of Equifax is 37.70, which means that it is trading at a less expensive P/E ratio than the market average P/E ratio of about 134.63.
The P/E ratio of Equifax is 37.70, which means that it is trading at a less expensive P/E ratio than the Business Services sector average P/E ratio of about 255.26.
Equifax has a P/B Ratio of 7.36. P/B Ratios above 3 indicate that a company could be overvalued with respect to its assets and liabilities.
About Equifax (NYSE:EFX) Stock
Equifax, Inc. engages in the provision of information solutions and human resources business process outsourcing services. It operates through the following business segments: U.S. Information Solutions, Workforce Solutions and International. The U.S. Information Solutions segment includes consumer and commercial information services, mortgage loan origination information, financial marketing services, and identity management. The Workforce Solutions segment covers employment, income, and social security number verification services as well as complementary payroll-based transaction and employment tax management services. The International segment offers information, technology, and services to support debt collections and recovery management in Canada, Europe, Latin America and Asia Pacific. The company was founded by Cator Woolford and Guy Woolford in 1899 and is headquartered in Atlanta, GA.
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EFX Stock News Headlines
Visa (V) Q1 Earnings and Revenues Top Estimates
The Next Big Crisis Is Here
You just can't see it yet because it's NOT a banking, financial, or economic crisis… it's far worse and threatens every dollar in your retirement account.
Equifax Inc. (NYSE:EFX) Receives Consensus Rating of "Hold" from Analysts
Jefferies Financial Group Weighs in on Equifax Inc.'s Q1 2023 Earnings (NYSE:EFX)
January 17, 2023 | benzinga.com
Golden Cross Appears Before Equifax Investors
Equifax (EFX) Gains 13.2% in the Past 6 Months: Here's How
Equifax Inc. (NYSE:EFX) Shares Could Be 44% Below Their Intrinsic Value Estimate
Equifax Launches Award-Winning I-9 Management Solution in the Mindbody Partner Store
Consumer complaints about credit reporting agencies highlighted in CFPB report
Credit reporting firms should fix practices amid consumer complaints- U.S. watchdog
Investing in Equifax (NYSE:EFX) five years ago would have delivered you a 66% gain
Do You Think Equifax (EFX) Can Maintain its Growth?
Equifax Makes Offer to Acquire Boa Vista Serviços in Brazil for R$8 Per Share
Equifax Announces December 19 Investor Call to Discuss Company's Offer to Acquire Boa Vista Serviços
Equifax Announces 2022 Developer Challenge and Accelerator Program Finalists
Total Consumer Debt Climbs to $2.36 Trillion as Consumers Lean on Credit Cards
November 25, 2022 | benzinga.com
Warner Music To Rally Around 17%? Plus This Analyst Predicts $223 For Equifax
November 25, 2022 | investing.com
Equifax PT Raised to $223 at Baird
November 24, 2022 | finance.yahoo.com
Visa (V) Up 4.1% Since Last Earnings Report: Can It Continue?
Consumer credit rating firms need reform, says UK watchdog
UPDATE 1-Consumer credit rating firms need reform, says UK watchdog
UK watchdog calls for reform of credit rating market
Equifax (EFX) Up 32.5% Since Last Earnings Report: Can It Continue?
Most Canadians Plan to Spend Less on Gifts this Holiday Season
Equifax (NYSE:EFX) Has Announced A Dividend Of $0.39
EFX Company Calendar
Ex-Dividend for 12/15 Dividend
Next Earnings (Estimated)
Consumer credit reporting agencies, mercantile reporting agencies,
Research & Consulting Services
www.equifax.com
$744.20 million
$4.92 billion
Mark W. Begor
John W. Gamble
EVP, Chief Financial & Operations Officer
Bryson R. Koehler
EVP, Chief Technology, Data & Analytics Officer
John J. Kelley
Secretary, Chief Legal Officer & EVP
Julia A. Houston
EVP, Chief Strategy & Marketing Officer
NYSE:TRU
NYSE:IT
Verisk Analytics
NASDAQ:VRSK
Aptiv
NYSE:APTV
NYSE:GPN
Sumitomo Mitsui DS Asset Management Company Ltd
Tokio Marine Asset Management Co. Ltd.
Bought 322 shares on 1/26/2023
Inspire Investing LLC
Strategic Blueprint LLC
Bought 1,587 shares on 1/26/2023
Eagle Bay Advisors LLC
EFX Stock - Frequently Asked Questions
Should I buy or sell Equifax stock right now?
16 Wall Street research analysts have issued "buy," "hold," and "sell" ratings for Equifax in the last twelve months. There are currently 1 sell rating, 7 hold ratings and 8 buy ratings for the stock. The consensus among Wall Street research analysts is that investors should "hold" EFX shares. A hold rating indicates that analysts believe investors should maintain any existing positions they have in EFX, but not buy additional shares or sell existing shares.
View EFX analyst ratings or view top-rated stocks.
What is Equifax's stock price forecast for 2023?
16 Wall Street research analysts have issued 12 month price targets for Equifax's shares. Their EFX share price forecasts range from $150.00 to $245.00. On average, they expect the company's stock price to reach $206.13 in the next twelve months. This suggests that the stock has a possible downside of 5.1%.
View analysts price targets for EFX or view top-rated stocks among Wall Street analysts.
How have EFX shares performed in 2023?
Equifax's stock was trading at $194.36 at the start of the year. Since then, EFX stock has increased by 11.7% and is now trading at $217.18.
When is Equifax's next earnings date?
The company is scheduled to release its next quarterly earnings announcement on Wednesday, February 8th 2023.
View our EFX earnings forecast.
How were Equifax's earnings last quarter?
Equifax Inc. (NYSE:EFX) released its earnings results on Tuesday, October, 19th. The credit services provider reported $1.85 earnings per share for the quarter, topping the consensus estimate of $1.72 by $0.13. The credit services provider earned $1.22 billion during the quarter, compared to analysts' expectations of $1.18 billion. Equifax had a net margin of 13.72% and a trailing twelve-month return on equity of 25.88%. The business's revenue for the quarter was up 14.5% on a year-over-year basis. During the same period last year, the firm posted $1.87 earnings per share.
How often does Equifax pay dividends? What is the dividend yield for Equifax?
Equifax announced a quarterly dividend on Thursday, November 3rd. Stockholders of record on Wednesday, November 23rd will be paid a dividend of $0.39 per share on Thursday, December 15th. This represents a $1.56 dividend on an annualized basis and a yield of 0.72%. The ex-dividend date of this dividend is Tuesday, November 22nd.
Read our dividend analysis for EFX.
Is Equifax a good dividend stock?
Equifax (NYSE:EFX) pays an annual dividend of $1.56 per share and currently has a dividend yield of 0.72%. The dividend payout ratio is 27.08%. This payout ratio is at a healthy, sustainable level, below 75%. Based on earnings estimates, EFX will have a dividend payout ratio of 20.69% next year. This indicates that the company will be able to sustain or increase its dividend.
What guidance has Equifax issued on next quarter's earnings?
Equifax issued an update on its fourth quarter 2022 earnings guidance on Thursday, November, 3rd. The company provided EPS guidance of $1.45-$1.55 for the period, compared to the consensus estimate of $1.65. The company issued revenue guidance of $1.17 billion-$1.19 billion, compared to the consensus revenue estimate of $1.20 billion.
What is Mark Begor's approval rating as Equifax's CEO?
228 employees have rated Equifax Chief Executive Officer Mark Begor on Glassdoor.com. Mark Begor has an approval rating of 73% among the company's employees.
What other stocks do shareholders of Equifax own?
Based on aggregate information from My MarketBeat watchlists, some companies that other Equifax investors own include Hawkins (HWKN), Micron Technology (MU), Mastercard (MA), NVIDIA (NVDA), Alibaba Group (BABA), Gilead Sciences (GILD), Johnson & Johnson (JNJ), Procter & Gamble (PG), Bank of America (BAC) and Starbucks (SBUX).
What is Equifax's stock symbol?
Equifax trades on the New York Stock Exchange (NYSE) under the ticker symbol "EFX."
Who are Equifax's major shareholders?
Equifax's stock is owned by a variety of retail and institutional investors. Top institutional shareholders include AKO Capital LLP (0.98%), Allspring Global Investments Holdings LLC (0.19%), Ceredex Value Advisors LLC (0.16%), ZWJ Investment Counsel Inc. (0.13%), Artemis Investment Management LLP (0.07%) and Vestmark Advisory Solutions Inc. (0.02%). Insiders that own company stock include Bryson R Koehler, John J Kelley III, John T Hartman, John W Gamble Jr, John W Gamble, Jr, Julia A Houston, Lisa M Nelson, Mark W Begor, Melissa D Smith, Prasanna Dhore and Sid Singh.
How do I buy shares of Equifax?
Shares of EFX stock can be purchased through any online brokerage account. Popular online brokerages with access to the U.S. stock market include WeBull, Vanguard Brokerage Services, TD Ameritrade, E*TRADE, Robinhood, Fidelity, and Charles Schwab.
What is Equifax's stock price today?
One share of EFX stock can currently be purchased for approximately $217.18.
How much money does Equifax make?
Equifax (NYSE:EFX) has a market capitalization of $26.59 billion and generates $4.92 billion in revenue each year. The credit services provider earns $744.20 million in net income (profit) each year or $5.76 on an earnings per share basis.
How many employees does Equifax have?
Does Equifax have any subsidiaries?
The following companies are subsidiares of Equifax: ASNEF/Equifax Servicios de Informacion Sobre Solvencia y Credito S.L., AccountScore, AccountScore Holdings Limited, AccountScore Limited, AccountScore US Corporation, Anakam, Anakam Inc., Anakam Information Solutions LLC, Ansonia Credit Data, Ansonia Credit Data Inc., Apac BizInfo Pte Limited, Appriss Insights, Appriss Insights LLC, Austin Consolidated Holdings Inc., Austin-Tetra, Barnett Associates Operations LLC, Bureau of Credit Histories Equifax Limited Liability Company, CDB Infotek, Compliance Data Center LLC, Computer Ventures Inc., Consents Online Limited, Corporate Services LLC, Credinformacoes Informaçoes de Credito Lda, Creditworks Australia Pty Ltd, Crime Finders LLC, Data-Crédito, DataVision Resources, DataVision Resources LLC, DataX, DataX Ltd., Datalicious Pty Ltd, Datum, EDX Australia Pty Limited, EFX de Costa Rica S.A., Efficient Hire, Equiecua Analytics Services of Risk S.A., Equifax (NZ) Holdings Pty Ltd, Equifax APAC Holdings Limited, Equifax Acquisition Holdings LLC, Equifax Americas S.C.S., Equifax Analytics FZE, Equifax Analytics Private Limited, Equifax Argentina S.A., Equifax Australasia Credit Ratings Pty Limited, Equifax Australasia Group Services Pty Limited, Equifax Australasia HR Solutions Pty Limited, Equifax Australasia Workforce Solutions Pty Limited, Equifax Australia CDR Pty Limited, Equifax Australia Commercial Services and Solutions Pty Limited, Equifax Australia Decision Solutions Pty Limited, Equifax Australia Group Pty Limited, Equifax Australia Holdings Pty Ltd, Equifax Australia Information Services and Solutions Pty Limited, Equifax Australia Marketing Services Pty Limited, Equifax Australia Personal Solutions Pty Limited, Equifax Australia Pty Ltd, Equifax Cambodia Holdings Pte Limited, Equifax Canada Co., Equifax Canadian Holdings II Co., Equifax Centroámerica S.A. de C.V., Equifax Commercial Services Limited, Equifax Consumer Services LLC, Equifax Credit Information Services Private Limited, Equifax Data Services LLC, Equifax EUA Limited, Equifax Ecuador C.A. Buró de Información Crediticia, Equifax Enterprise Services LLC, Equifax Europe LLC, Equifax Fraude S.L., Equifax Funding LLC, Equifax Holdings (NZ) Limited, Equifax Honduras Central de Riesgo Privada S.A., Equifax Iberica S.L., Equifax Information Services LLC, Equifax Information Services of Puerto Rico LLC, Equifax Information Technology LLC, Equifax International Treasury Services Unlimited Company, Equifax Limited, Equifax Luxembourg (No. 10) S.àr.l., Equifax Luxembourg (No. 3) S.àr.l., Equifax New Zealand Holdings Limited, Equifax New Zealand Information Services and Solutions Limited, Equifax Paraguay S.A., Equifax Peru S.A., Equifax Pty Limited, Equifax South America LLC, Equifax Spain Holdings S.àr.l., Equifax Special Services LLC, Equifax Technology (Ireland) Limited, Equifax Technology Solutions LLC, Equifax UK AH Limited, Equifax Uruguay S.A., Equifax do Brasil Ltda., Forseva LLC, GetCreditScore Pty Ltd, Grupo Inffinix S.A. de C.V., HD Information LLC, HIREtech, HealthCare Impact Associates, HealthCare Impact Associates II LLC, HealthCare Impact Associates L.L.C., ID Rehab Holdings Inc., ID Watchdog, IDR Processing LLC, IXI, IXI Corporation, Identity Rehab Corporation, IdentityProtection.com, Inffinix Software, Inffinix Software Comercio Servicios Importação e Expostação Ltda., Inffinix Software S.A. de C.V., Innovative Enterprises LLC, Integrated Debt Services Ltd., IntelliReal, IntelliReal LLC, Inversiones Equifax Chile Limitada, JLR Inc., Knowledge Works Inc., Kount, Kount Inc., Mapcity Peru S.A.C., Mapcity.com Chile S.A., Net Profit Inc., Nevalon Technologies LLC, Paradigm National Consultants LLC, PayNet Inc., Paynet, Pioneer Holdings Limited, Plantation RE Holdings LLC, Rapid Reporting, Rapid Reporting Verification Company LLC, ReachTEL Pty Ltd, Redbird Insurance LLC, Secure Sentinel Australia Pty Limited, Securitec Screening Solutions LLC, Servicios Equifax Chile Limitada, T1 Ventures LLC, TALX Corporation, TALX UCM Services Inc., TDX Group Limited, TDX Indigo Iberia SL, Teletrack, Teletrack LLC, The Prospect Shop Pty Ltd, TrustedID Inc., Typhoon Data LC, VA (NZ) Holdings Limited, VA Australia Finance Pty Limited, Veda Advantage, Verdad Informatica de Costa Rica S.A., Worxtime LLC, ZIP ID Pty Ltd, eThority LLC, ethority, and i2Verify.
How can I contact Equifax?
Equifax's mailing address is 1550 PEACHTREE STREET N.W., ATLANTA GA, 30309. The official website for the company is www.equifax.com. The credit services provider can be reached via phone at (404) 885-8000, via email at trevor.burns@equifax.com, or via fax at 404-888-8682.
This page (NYSE:EFX) was last updated on 1/27/2023 by MarketBeat.com Staff


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Has America's Influence in the Middle East Really Declined?
December 18, 2021 Topic: Middle East Policy Region: Middle East Tags: Middle EastIranIsraelAfghanistanIraqSaudi ArabiaU.S. AlliesInterventionCold War
Forty years ago, U.S. allies raised similar concerns about how America's withdrawal from Indochina in 1973 and its "allowing" the downfall of the Shah in 1979 cast doubts on Washington's commitment to its other allies. But America didn't leave the Middle East then, and is not going to leave it now either.
by Mark N. Katz
It has become commonplace to read or hear from commentators that America's position in the Middle East has drastically declined. Some even see U.S. influence there as being on the way out altogether. But is U.S. influence in the Middle East really less now than it was in the past?
The U.S. withdrawal from Afghanistan and the collapse of the government it was supporting there, the end of U.S. combat operations in Iraq, the small remaining footprint that the United States has in Syria along with its inability to bring about meaningful political change there, and its difficult relationship with Turkey all point to less U.S. influence in the region than existed in the recent past.
But the post-9/11 period in which the U.S. militarily intervened and set up new governments in Afghanistan and Iraq, and later hoped to support positive change in Libya and Syria was an exceptional period during which the United States had—or appeared to have—much greater influence than now.
If, however, we compare U.S. influence in the Middle East now with what it was forty years ago at the height of the Cold War in 1981, what we find is that it is remarkably similar now to what it was then. In 2021, America has basically the same allies that it had in 1981: Israel, Egypt, Jordan, Saudi Arabia and all the other Gulf Arab monarchies, and Morocco. While still formally allied to Turkey, America's relationship with Ankara is quite awkward now—but it was back then too in the wake of the 1974 Turkish invasion of eastern Cyprus and its hostile relationship with another American ally, Greece.
Of course, comparing America's position today with what it was in 1981 is somewhat arbitrary. If we compared today with 1976 instead of 1981, Iran would have been in the list of U.S. allies—something it definitely is not now. But if we compared today with five years further back—1971—then Egypt would not have been in the list of Washington's allies, but Moscow's instead. What this shows is that the Cold War era—like the present one—was an era in which gaining and losing allies was normal.
Many of those who decry the loss of American influence in the Middle East point to the rise of Russian influence there. But compared to the past, Russia's comeback is not all that impressive. In 1981, the Soviet Union was the superpower with predominant influence in Syria, Iraq, South Yemen, Libya, and Afghanistan. It also had much closer relations with Algeria and North Yemen than the United States did. Now, by contrast, Russia shares influence with Iran in Syria and with Turkey and others in Libya. It has only limited influence in Afghanistan, Yemen, and Iraq.
Some might see the growing ties that Moscow and Beijing each have developed with America's Middle Eastern allies as something that Washington should worry about. During the Cold War, though, the Soviet Union was actively trying to weaken or even overthrow governments allied to the United States. Now, both Russia and China want to work with all Middle Eastern governments allied to the United States, not weaken them. Indeed, neither Russia nor China even seems to be trying to get Middle Eastern governments to end their alliances with the United States and ally with either or both of them instead. In fact, neither of America's great power rivals seems eager to replace the United States as the security guarantor for America's Middle Eastern allies. Washington having to compete with Moscow and Beijing for arms sales, oil deals, and investments from America's own allies might be annoying, but these are much less serious problems than having to counter previous Soviet efforts to weaken or overthrow them were.
Whether Turkey remains allied to the United States, though, is a question that has arisen, not least because of its growing cooperation with Moscow—especially through its purchase of Russian S-400 air defense missiles against Washington's strong objections. But just because Turkey's alliance with the United States has grown weaker does not mean that it is becoming a Russian ally. Turkey, after all, is at odds with Russia in Syria, Libya, the Armenia-Azerbaijan theater, and even Ukraine. Turkey, it seems, is not so much interested in being either America's or Russia's ally than in being a great power in its own right. This is something that poses a challenge not just for Washington, but also for Moscow and for both of their regional allies.
The vision of the United States as the predominant power in the Middle East that took hold in the immediate afterglow of what at first seemed to be America's successful interventions in Afghanistan and then Iraq did not last all that long. But America still has basically the same allies in the Middle East that it had forty years ago. And so long as it does, America can remain a great power in the Middle East so long as it wants to.
Several of America's Middle Eastern allies, though, point to the downfall of the Kabul government in Afghanistan and the rise of Iranian influence in Iraq as casting doubt on America's willingness to remain a great power in the Middle East. But forty years ago, those same allies raised similar concerns about how America's withdrawal from Indochina in 1973 and its "allowing" the downfall of the Shah in 1979 cast doubts on Washington's commitment to its other allies. But America didn't leave the Middle East then, and is not going to leave it now either.
Mark N. Katz is a professor of government and politics at the George Mason University Schar School of Policy and Government, and a nonresident senior fellow at the Atlantic Council.
Image: Flickr.


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Home » End of Life Doula UK Blog » Talking about and Reflecting on Death » Why I make Films about Death – Barry J Gibb Film Director
Why I make Films about Death – Barry J Gibb Film Director
27/06/2022 29/02/2020 by Lizzie
I absolutely love making films. I've worked in a lab, teasing apart the cellular basis of life and written a book about the brain but the act of capturing real life, then editing it to create a story reigns supreme. And, while it's lovely to get paid to make films, there are some I do purely for love, out of curiosity. I wanted to share a personal behind the scenes about one of those films now…
My first vivid memory is of death… Like the memory of a memory, it appears as fractured scenes. My mother and I are at home, by the front door, in the hall. Like a nightmare, the memory feels darker than it should. Or brighter. Bent over to bring our faces together and through an endless river of tears, my mother is explaining to me that my grandfather, her father, is dead.
I do not recall feeling sadness. It was terror. Too young to care about any other living entity, the fact my mother had lost her father made no impact. Instead, awareness flooded into me, a dark knowledge that my precious little life could, in fact, be snuffed out by some unseen, unstoppable force. And then I screamed, 'I don't want to die!', over and over, like a mantra to Death, hoping it would hear me over the sobs of my mother, take pity on this poor child and leave me to eternally play with my toys in a world filled with love and light.
Death has always roamed my thoughts. A silent companion encouraging me to eat well, not to smoke, to run, to look both ways at roads… It's probably what nudged me to study the very essence of life, the biochemistry that drives our cells as they wage war on entropy, on death.
This fascination with death grew into a healthy love of horror. Of zombies, demons and serial killers that gave a shape and form to death. That turned death into a foe with a face you could battle and, on occasion, defeat. In its brilliantly urgent and visceral way, horror was the first time I realised death could be conquered. It's in this tension between the living and not living that I've found my creative home. From the metabolic processes igniting the smallest of cells to the orchestrated symphony of synaptic pathways generating what we feel as imagination or love.
And this may be the only life there is. On Earth, it is ubiquitous, abundant, verdant and gloriously out of control. It is viral, bacterial, photosynthetic and metabolic. It has teeth and limbs and gills and wings – it soars.
My calling is to create films that simultaneously act as a reminder of life's magnificence while acknowledging its impermanence.
As far as we know, life on this planet may be all there is in the Universe. It's so easy to forget, in the midst of headlines, apps and emails just how rare and precious this all is. My calling is to create films that simultaneously act as a reminder of life's magnificence while acknowledging its impermanence. That highlight the greatness we can aspire to in the face of our own fleeting lifetime – hope in the absence of hope.
The first film I made a genuine attempt to span these worlds was, 'Until', a short documentary exploring mortality, immortality and the science of ageing. At the heart of the film sits a single question, if science becomes so advanced you could choose your own lifespan, at what age would you choose to die?
Filled with heart, humour and some beautifully honest insights supplied by scientists, children and the elderly, it's still one of my favourites and received an 'Audience Award' at the Imagine Science Film Festival in New York.
More recently, this fascination with life's finite nature expressed itself as an obsession with the fabric and perceptions of time. The indie films I make are largely experiments – an attempt to understand people, subjects and filmmaking at a deeper level. And so, with The Horologist, I was allowed to delve into the world of watchmaking, an ongoing fascination, while probing the watchmaker for his more philosophical thoughts regarding human behaviour and time.
This led me to wonder how those aware of their own mortality might view time and, in turn, this curiosity steered me back to Living Well Dying Well (LWDW), an organisation I'd made a short film with before. LWDW supports and trains 'End of Life Doulas', remarkable people who help those aware of their own mortality – and their families – navigate their dwindling time on Earth in the best possible way.
We are bad at death. I'm not sure my ability to 'deal' with death has advanced terrifically since my grandfather vanished. Death lands like a tornado, indiscriminately destroys our world, casts aside those that we love and moves on, leaving emotional devastation. End of Life Doulas can transform the tornado into a gentle breeze, a celebration of the past, of the now, of the end.
They introduced me to Peter, a wonderful man living with heart failure. Together, we explored the mysteries of time and life as his parrot eyed me silently, begrudging my time with his master. Peter, a former policeman, had long retired and now spent his remaining days painting. He paints his dreams, he paints his imagination and he paints scenes from his lives…
One painting, The Life I Lived, revealed a chronological tapestry of his life. From birth to death these memories-as-art formed delicate bubbles of moments highlighting key events from his time on Earth. Then he floored me by casually showing me its artistic partner, The Life I Didn't Live, also the title of the short film I made. The manifestation of his love fulfilled, regrets undone and lost dreams found. It was striking in its purity of heart.
Shortly after meeting Peter, LWDW contacted me to introduce me to another person living with the knowledge of their own mortality. Which is how I met the artist, Barbara Bird, beginning an all too brief friendship and journey towards death and beyond. But that's a story for another time.
Emma Dixon – No Fear but only Love
It's a great Dog's Life!