text:
\section{Introduction}
\label{intro}
It is widely accepted that the observable universe originates from an early homogeneous phase beginning presumably around the Planck scale, just after a less understood phase of quantum spacetime. This homogeneous phase has a classical description by an effective FLRW model with scalar matter. The subsequent inhomogeneity is attributed to quantum fluctuations of space that induce matter inhomogeneities that grow, and loss coherence due to inflation. Thus, a quantum treatment seems to be natural for the homogeneous phase.

Standard quantum cosmology is based on the canonical quantization of general relativity~\citep{Hartle}. Following Dirac, the Hamiltonian constraint, generator of time reparametrizations, is implemented as a time-independent Schr\"odinger equation, the Wheeler--DeWitt (WDW) equation. Additionally, the solution to the WDW equation, i.e., the wave function of the universe, must be supplemented with a prescription to compute probabilities considering the singular character of the universe. Further, as the Hamiltonian operator annihilates the wave function, this is a timeless theory. However, the universe exhibits a marked one-way evolution (arrow of time), and internal observers have clocks \citep{tiempo,Kuchar,Isham,Anderson}.

In recent years, there have been several proposals in standard quantum cosmology that mainly relate time to the scale factor, essentially by a gauge fixing. These proposals involve mostly approximations of the semiclassical type, as well as Born--Openheimer with a weakly coupled matter sector and a large-scale factor. In~\citep{barvisnky}, a general gauge fixing was analyzed, which was applied in~\citep{barvisnkyk} to several minisuperspace models with a classical `extrinsic' time. In~\citep{venturi98}, a Born--Oppenheimer approximation was used to separate the scale factor from a weakly coupled matter sector. This allowed for defining a time as in the WKB approach, proportional to the square of the scale factor, and parametrize matter evolution with an effective Hamiltonian; see also~\citep{moniz1,moniz2}. Further, in~\citep{venturi98} and a subsequent series of works, increasingly complex settings were  analyzed, an inflaton with a mass term in~\citep{venturi98}, additional generic matter in~\citep{venturi03}, Mukhanov--Sasaki scalar perturbations for a de Sitter evolution in~\citep{venturi13}, and tensor perturbations in a general slow-roll inflationary setting in~\citep{venturi14}. The parameter values of the last work were restricted in~\citep{venturi15} by comparison with observational data, and in~\citep{venturi16}, they  were considered  effects on the spectra of primordial perturbations. In~\citep{venturi18} the consequences of the interference of the wave functions before and after a bounce were analyzed. For supersymmetric quantum cosmology, in~\citep{moniz1,moniz2,obregon2}, in the semiclassical approach, the effect of supersymmetry was explored for the solution.

The purely bosonic Wheeler--DeWitt equation is a second-order partial differential equation (PDE) in (mini)superspace. To single out a solution that corresponds to the wave function of the universe, one must impose suitable boundary conditions.  Defining the appropriate boundary conditions that give rise to the universe with which we are familiar  constitutes a well-known fundamental problem in quantum cosmology. There is also the possibility  that a more complete theory introduces additional restrictions that uniquely determine a quantum state. An example of this is quantum supersymmetric cosmology; see, e.g.,~\citep{moniz1,moniz2}. In this case, the most general state has multiple components, and the Hamiltonian constraint amounts to a system of coupled second-order PDEs that is equivalent to a system of first-order PDEs, the supersymmetric constraints. In~\citep{previo:2016}, we worked out a supersymmetric model leading to an analytic solution to the WDW equation. In the present work, with a slightly simpler WDW equation by a different operator ordering, we consider the time choice of~\citep{previo:2016} by analyzing the wave function. The general expression of this wave function allows for the identification of a curve of most probable values in configuration space (superspace), parametrized by the scalar field, and suggests to choose it as time. Such a type of choice has been known for a long time~\citep{banks}. Here, we analyze in detail the wave function regarding the choice  in~\citep{previo:2016}, of an effective time-dependent wave function with a probability density that corresponds to the conditional probability of measuring a value of the scale factor for a given value of the scalar field. Thus, the mean values computed with this wave function were time-dependent, in particular for the scale factor, which gives a trajectory that follows closely the previously mentioned curve of most probable values. Further, we consider the quantum cosmology of this approach, and explore a family of inflationary solutions.

We consider supersymmetric models because, even if at LHC energies, supersymmetry has not been found, it might be broken at higher energies, and it continues to be part of important candidates of ultraviolet completions for quantum gravity, supergravity, and string theory. Supersymmetry nontrivially relates   fermions and bosons; in a supersymmetric quantum field theory, fermionic and bosonic divergences are cancelled~\citep{wess}.
Thus, supersymmetric quantum cosmology~\citep{obregon0,eath,moniz-1,moniz-2} is a relevant option for the study of quantum cosmology. Supersymmetry can be formulated by the extension of spacetime translations to translations in a Grassmann-extended spacetime, which includes fermionic coordinates, called superspace\footnote{Should not be confused with the superspace of geometrodynamics.}. The fields on this supersymmetry superspace are called superfields, and supergravity can be formulated as a general relativity theory on a supermanifold~\citep{wess,cupa}. There are several formulations for supersymmetric extensions of homogeneous cosmological models~\citep{eath,moniz-1}. One class of such formulations comes from a dimensional reduction of four- or higher-dimensional supergravity theories by considering homogeneous fields depending only on time and integrating the space coordinates~\citep{ryan}. The other class is obtained by supersymmetric extensions of homogeneous models, invariant under general reparametrizations of time~\citep{graham,graham1,graham2}, or invariant under general reparametrizations on a superspace, with anticommutative coordinates besides time~\citep{tkachwf,previo}. In~\citep{previo:2016,previo}, we followed~\citep{cupa}, where one of us gave a geometric Lorentz covariant superfield model building tool for supergravity that can be straightforwardly applied to any number of spacetime dimensions. In particular, a homogeneous formulation could be straightforwardly traced back to four-dimensional supergravity.

As usual in theories with fermionic degrees of freedom, their conjugate momenta are eliminated by solving a number of second-class constraints, leaving an algebra of Dirac brackets. The corresponding quantum fermionic operators can be represented in several ways, e.g., by a matrix representation~\citep{obregon0,obregon1},  representing half the fermionic degrees of freedom by either differential operators~\citep{eath2}, or by creation operators acting on a vacuum state~\citep{graham2,previo:2016}. The wave function is spinorial in the first case, or a finite expansion of possible states in the second case. In any case, the Wheeler--DeWitt equation is equivalent to a system of first-order partial differential equations. In many cases, they have exact solutions~\citep{tkachwf,obregon1,previo}, and the integration constants can be assimilated in the normalization. Therefore no initial conditions are required, although the state  depends on the model. For supersymmetric extensions of higher-order theories, such as $f(R)$ theories, the differential equations might not be first-order~\citep{nephtali}.

In Section \ref{FLRW}, we review the superfield formulation of supersymmetric cosmology. In Section \ref{quantization}, we review the quantization of the models from~\citep{previo:2016};  supersymmetric Wheeler--DeWitt equations have an analytic solution that depends on the scale factor and the superpotential. In Section \ref{time}, we discuss the problem of time. The identification of high-probability paths in configuration space to which mean trajectories correspond leads to the identification of the scalar field as time. Thus, following~\citep{previo:2016}, a time-dependent effective wave function can be given. This effective wave function allows for computing mean values of the scale factor that give a time evolution. This scale factor is inversely proportional to the cubic root of the superpotential, and we obtain inflationary behavior for a family of superpotentials, as shown in Section \ref{inflation}. These superpotentials depend on three parameters, namely, $\mu$, $\lambda$, and $p$; the first  determines the time scale, the second  the number of $e$-folds, and the last is a power that modifies the initial conditions of the scale factor. After fixing  parameters $\mu$ and $\lambda$, we compute the tensor/scalar ratio and the scalar spectral index  with remarkably good agreement with the observational bounds of PLANCK observatory without having to adjust parameters for this purpose. Lastly, in Section \ref{discussion}, we  present a short discussion with some remarks and future work perspectives. In an appendix, we give the effective wave function and the scale factor for $k=1$.

\section{Supersymmetric FLRW Model with a Scalar Field}
\label{FLRW}

The large-scale observable universe has been modeled in general relativity by the FLRW metric with scalar fields. This is  quite a general setting that could follow from a fundamental theory, and can account for inflation, primordial matter generation and structure formation, and dark energy. We consider the most studied model, the simplest, with a single minimally coupled scalar field $\frac{1}{2\kappa^2}\int\sqrt{-g}Rd^4x+\int\sqrt{-g}[\frac{1}{2}\partial^\mu\phi\partial_\mu-V(\phi)]d^4x$, where $\kappa^2=\frac{8\pi G}{c^4}$. For the FLRW metric, it reduces to  well-known form
\begin{equation}
	I=\frac{1}{\kappa^{2}}\int\left\{  -\frac{3}{c^2}N^{-1}a\dot{a}^{2}+3Nka-Na^3\Lambda+\kappa^{2}a^{3}\left[\frac{1}{2c^2}N^{-1}\dot{\phi}^{2}-NV\left(\phi\right)\right]\right\}dt.
	\label{actioncosmo}
\end{equation}

This Lagrangian is invariant under general time reparametrizations. From this action, follow the Friedmann equations and the conservation equation for a perfect fluid described by  scalar field $\phi(t)$, i.e., in natural units and comoving gauge,
$\frac{\dot{a}^{2}}{a^{2}}-\frac{\Lambda}{3}+\frac{k}{a^2}=\frac{\kappa^{2}}{3}\rho$, $\frac{2\ddot{a}}{a}+\frac{\dot{a}^{2}}{a^{2}}-\Lambda+\frac{k}{a^2}=-\kappa^{2}p$ and
$\dot{\rho}+\frac{3\dot{a}}{a}(p+\rho)=0$,
with $\rho=\frac{1}{2} \dot{\phi}^{2}+V(\phi)$ the energy
density, and $p=\frac{1}{2} \dot{\phi}^{2}-V(\phi) $ the pressure for the
perfect fluid $\phi(t)$.
The momenta are $\pi_a=-\frac{6}{c^2\kappa^{2}}N^{-1}a\dot{a}$ and $\pi_\phi=-\frac{1}{c^2}N^{-1}a^3\dot{\phi}$
The Hamiltonian is $H=NH_0$, where $H_0$ is the Hamiltonian  constraint,
which generates time reparametrizations.

\subsection{Supersymmetric Cosmology}
Supergravity, the supersymmetric version of gravity, can be formulated as general relativity in superspace, an extension of spacetime by anticommutative spinorial variables, in four dimensions, $x^m\to(x^m,\theta_\alpha,\bar{\theta}^{\dot{\alpha}})$, where $\theta$ are Weyl spinors and $\bar{\theta}$ their conjugates~\citep{wess}, $\alpha, \dot{\alpha}=1,2$. Supersymmetric field theory on superspace realizes supersymmetry algebra
$\left\{Q_\alpha,\bar{Q}_{\dot{\alpha}}\right\}=2i\sigma^m_{\alpha\dot{\alpha}}\partial_m$, which extends the Poincar\'e algebra. Thus, for homogeneous fields, the charges decompose into two copies
\begin{equation}
	\left\{Q_\alpha,\bar{Q}_{\dot{\alpha}}\right\}=2i\sigma^0_{\alpha\dot{\alpha}}\partial_0=2i\delta_{\alpha\dot{\alpha}}\partial_0.
\end{equation}

Therefore, a minimal version of homogeneous supersymmetric field theory can be given by extending time by one complex anticommuting coordinate, which amounts to supersymmetric quantum mechanics. This theory can be obtained, in general, by dimensional reduction from higher-dimensional models to one (time) dimension~\citep{halpern}. Thus, supersymmetric cosmology can be obtained from one-dimensional supergravity~\cite{tkachwf}.

For the sake of clarity, here we shortly review the derivation of the supersymmetric Wheeler--DeWitt equation following~\citep{previo,previo:2016}. In these works, we formulated it as general relativity on supersymmetry--superspace,
$t\rightarrow z^{M}=(t,\Theta,\bar{\Theta})$, where $\Theta$ and $\bar{\Theta}$
are the anticommuting coordinates, the so-called "new" $\Theta$-variables~\citep{wess}. Hence, under $z^{M}\rightarrow z^{\prime M}=z^{M}+\zeta^{M}(z)$, the superfields,  see e.g.,~\cite{wess,cupa},
transform as $\delta_{\zeta}\Phi(z)=-\zeta^{M}(z)\partial_{M}\Phi(z)$,
and their covariant derivatives are $\nabla_{A}\Phi={\nabla_{A}^{\ M}(z)\partial_{M}}\Phi$. $\nabla_{A}^{\ M}(z)$ is the superspace vielbein,
whose superdeterminant gives the invariant superdensity
$\mathcal{E}=\mathrm{Sdet}{\nabla_{M}}^{A}$, $\delta_{\zeta}\mathcal{E}=(-1)^{m}\partial_{M}(\zeta^{M}\mathcal{E})$.
For the supersymmetric extension of the FLRW metric, we have $\mathcal{E}=-N-\frac{i}{2}(\Theta\bar{\psi}+\bar{\Theta}\psi)$ \cite{previo}. In this formulation, to the scale factor and the scalar field correspond real scalar superfields~\citep{wess,tkachwf}.
\begin{align}
	\mathcal{A}\left(  t,\Theta,\bar{\Theta}\right)  =a\left(  t\right)
	+\Theta{\lambda}\left(  t\right) -\bar{\Theta}\bar\lambda\left(  t\right)
	+  \Theta\bar{\Theta}B\left(t\right),\\
	\Phi\left(  t,\Theta,\bar{\Theta}\right)  =\phi\left(  t\right)  +\Theta{\eta}\left(  t\right)
	-\bar{\Theta}\bar\eta(t)+\Theta\bar{\Theta}G\left(  t\right). \label{superfields}
\end{align}

The supersymmetric extension of Action (\ref{actioncosmo}) for $k=0,1$ is
$I=I_G+I_{M}$ , where $I_{G}$ is the supergravity action, and $I_M$ is the matter term \cite{tkachwf,superfield,previo:2016}
\begin{align}
	I_{G}&=\frac{3}{\kappa^{2}}\int\mathcal{E}\left(  \mathcal{A}\nabla
	_{\bar{\Theta}}\mathcal{A}\nabla_{\Theta}\mathcal{A}-\sqrt{k}\mathcal{A}^{2}\right)  d\Theta d\bar{\Theta}dt, \label{susyraction}\\
	I_{M}&=\int\mathcal{E}\mathcal{A}^{3}\left[  -\frac
	{1}{2}\nabla_{\bar{\Theta}}\Phi\nabla_{\Theta}\Phi+W\left(  \Phi\right)
	\right]  d\Theta d\bar{\Theta}dt, \label{susymaction}
\end{align}
where $W$ is the superpotential.
\subsection{Component Formulation}
\label{componentform}
The component action follows from (\ref{susyraction}) and (\ref{susymaction}). After performing the Grassmann integrals, integrating out  auxiliary fields $B$ and $G$, and producing the redefinitions
$\lambda\rightarrow a^{1/2}\lambda$, $\bar{\lambda}\rightarrow a^{1/2}\bar{\lambda}$,
$\eta\rightarrow a^{3/2}\eta$, and $\bar{\eta}\rightarrow a^{3/2}\bar{\eta}$, the Lagrangian reads, see~\citep{previo:2016}
\begin{align*}
		L  =-\frac{3a\dot{a}^{2}}{c^2N\kappa^{2}}+\frac{a^{3}\dot{\phi}^{2}}{2c^2N}
		+\frac{3kNa}{\kappa^{2}}-3\sqrt{k}Na^{2} W+\frac{3N\kappa^{2}}{4}a^{3}W^{2}-\frac{1}{2}a^{3}N{W'}^{2}
		+\frac{3i}{c\kappa^{2}}\left(  \lambda\dot{\bar{\lambda}}+\bar{\lambda}\dot{\lambda}\right)
		-\frac{i}{2c}\left(  \eta\dot{\bar{\eta}}+\dot{\eta}\bar{\eta}\right) \\
		+\frac{3\sqrt{a}\dot{a}}{c\kappa^2N}\left(  \psi\lambda-\bar{\psi}\bar{\lambda}\right)
		-\frac{a^{3/2}\dot{\phi}}{2cN}\left(  \psi\eta-\bar{\psi}\bar{\eta}\right)
		+\frac{3i\dot{\phi}}{2c}\left(  \lambda\bar{\eta}+\bar{\lambda}\eta\right)
		+3N\left(\frac{\sqrt{k}}{\kappa^{2}a}-\frac{3}{2}W\right)\lambda\bar{\lambda}
		+N\left(-\frac{3\sqrt{k}}{2a}+\frac{3\kappa^{2}}{4}W-W''\right)\eta\bar{\eta} \\
		+3ia^{3/2}\left(\frac{\sqrt{k}}{\kappa^2a}-\frac{1}{2}W\right)\left(  \psi\lambda+\bar{\psi}\bar{\lambda}\right)
		-\frac{ia^{3/2}}{2}W'\left(  \psi\eta+\bar{\psi}\bar{\eta}\right)
		-\frac{3N W'}{2}\left(  \lambda\bar{\eta}-\bar{\lambda}\eta\right)
		-\frac{3}{2N\kappa^2}\psi\bar{\psi}\lambda\bar{\lambda}+\frac{1}{4N}\psi\bar{\psi}\eta\bar{\eta},
	\end{align*}
where $W\equiv W(\phi)$,  $W'\equiv \partial_\phi W(\phi)$, and $W''\equiv \partial_\phi^2 W(\phi)$.

The Hamiltonian is of the form $H=NH_{0}+\frac{1}{2}\psi S-\frac{1}{2}\bar{\psi}\bar{S}$, with the components of the one-dimensional supergravity multiplet $(N,\psi,\bar{\psi})$ as Lagrangean multipliers enforcing the Hamiltonian ($H_0\approx 0$) and supersymmetric ($S\approx 0$, $\bar{S} \approx 0$) constraints~\citep{previo:2016}.

The basic nonvanishing Dirac brackets are $\{a,\pi_{a}\}=\{\phi,\pi_{\phi}\}=1$, $\{\lambda,\bar{\lambda}\}_{+}=\frac{c\kappa^2}{6}$, $\{\eta,\bar{\eta}\}_{+}=-c$. With these brackets, one can verify the following algebra of constraints
\begin{align}
	\{S,\bar S\}_{+}&=-2H_0,\label{ss}\\
	\{H_0,S\}&=\{H_0,\bar S\}=0. \label{hs}
\end{align}

The scalar potential in the Hamiltonian $H_0$ is~\citep{previo:2016}
\begin{equation}
	V_S=\frac{3\sqrt{k}}{a}W-\frac{3\kappa^{2}}{4}W^{2} +\frac{1}{2}{W'}^{2}.\label{scalarpot}
\end{equation}

\textls[-15]{For $k=0$, the sign of the superpotential does not matter for the scalar~potential.}
\section{Quantization}
\label{quantization}
Homogeneous cosmology is a mechanical system; hence, it can be quantized with the formalism of ordinary quantum mechanics. There are, however, several well-known problems. On the one hand, the probabilistic character of measurements in quantum mechanics clashes with the uniqueness of the system as there is no ensemble of universes to perform a series of tests, in identical, observer shaped conditions~\citep{halliwell}. Nevertheless, observables such as the Hubble parameter can be determined by a set of observations. On the other hand, since the Hamiltonian vanishes, a time parameter cannot be introduced by means of the Schr\"odinger equation, or for the wave function or for the observables. Nonetheless, the Wheeler--DeWitt equation gives a time-independent Schr\"odinger equation with zero eigenvalue whose solution depends on the superspace variables, the minisuperspace in the homogeneous case, and gives the probability amplitude for the universe to be found in certain superspace configurations. The fact that the theory does not give a time evolution is the well-known consequence of invariance under time reparametrizations. Time is argued to be an internal property that can be determined by the choice of a clock~\citep{Kuchar}. On the other side, the observed universe is classical~\citep{halliwell}; hence, its description is given by mean values of the quantum operators. We further discuss the time problem in Section \ref{time}.
\subsection{Supersymmetric Wheeler--DeWitt Equations}
For the derivation of  supersymmetric Wheeler--DeWitt equations, we follow~\citep{previo:2016}, but with a different ordering for fermions which yields somewhat simpler solutions. For consistency,  the Hamiltonian operator must be Hermitian; hence, the supercharges must satisfy $\bar S=S^\dagger$ and  $S=\bar{S}^\dagger$. The only nonzero (anti)commutators are
\begin{equation}
	[a,\pi_{a}]=[\phi,\pi_{\phi}]=i\hbar,\qquad\{\lambda,\bar{\lambda}\}=\frac{4\pi}{3}l_P^2,\qquad\{\eta,\bar{\eta}\}=-\hbar c,  \label{conmutadores}
\end{equation}
where $l_P^2=\frac{\hbar G}{c^3}$ is the Planck length.
For the quantization, we redefine the fermionic degrees of freedom as
$\lambda=\sqrt{\frac{\hbar c\kappa^2}{6}}\alpha$, $\bar\lambda=\sqrt{\frac{\hbar c\kappa^2}{6}}\bar\alpha$, $\eta=\sqrt{\hbar c}\beta$
and $\bar\eta=\sqrt{\hbar c}\bar\beta$. Hence, the anticommutators are
\begin{equation}
	\qquad\{\alpha,\bar{\alpha}\}=1,\qquad\{\beta,\bar{\beta}\}=-1.  \label{conmutadoresf}
\end{equation}
as well as $\alpha^{2}=\beta^{2}=\bar{\alpha}^{2}=\bar{\beta}^{2}=0$.
The bosonic momenta are represented by derivatives, $\alpha$ and $\beta$ are
annihilation operators, and $\bar{\alpha}$ and $\bar{\beta}$ are creation operators.
We fixed the ordering ambiguities by Weyl ordering, which  is antisymmetric for fermions. Hence, the supersymmetric constraint operators read

\begin{align}
	\frac{1}{\sqrt{\hbar c}} S  & =\frac{c\kappa}{2\sqrt{6}}\left(a^{-\frac{1}{2}}\pi_a+\pi_a a^{-\frac{1}{2}}\right)\alpha
		+ca^{-\frac{3}{2}}\pi_\phi\beta
		+\frac{3i\kappa}{\sqrt{6}}  a^\frac{3}{2}W\alpha
		+i a^\frac{3}{2}W'\beta
		-i\frac{\sqrt{6k}}{\kappa}a^\frac{1}{2}\alpha
		-\frac{i\sqrt{3}}{4\sqrt{2}}\hbar c\kappa a^{-\frac{3}{2}}\alpha[\bar{\beta},\beta],\label{Squant}\\
		\frac{1}{\sqrt{\hbar c}} \bar S  & =\frac{c\kappa}{2\sqrt{6}}\left(a^{-\frac{1}{2}}\pi_a+\pi_a a^{-\frac{1}{2}}\right)\bar\alpha
		+ca^{-\frac{3}{2}}\pi_\phi\bar\beta
		-\frac{3i\kappa}{\sqrt{6}}  a^\frac{3}{2}W\bar \alpha
		-i a^\frac{3}{2}W'\bar \beta
		+i\frac{\sqrt{6k}}{\kappa}a^\frac{1}{2}\bar \alpha
		+\frac{i\sqrt{3}}{4\sqrt{2}}\hbar c\kappa a^{-\frac{3}{2}}\bar\alpha[\bar{\beta},\beta].\label{Sbquant}
	\end{align}

Anticommutator  $\{S,\bar S\}=-2\hbar c H_0$ gives the quantum Hamiltonian
	\begingroup\makeatletter\def\f@size{9.5}\check@mathfonts
	\def\maketag@@@#1{\hbox{\m@th\normalsize\normalfont#1}}
	\begin{align}
		H_0=&-\frac{c^2\kappa^2}{24}\left(a^{-1}\pi_a^2+\pi_a^2a^{-1}\right)+\frac{c^2}{2}a^{-3}\pi_\phi^2
		-\frac{\sqrt{3} i}{2\sqrt{2}}\hbar c^2\kappa a^{-3}\pi_\phi(\alpha\bar\beta+\bar\alpha\beta)-\frac{3k}{\kappa^2}a
		-\frac{\sqrt{k}}{4}\hbar ca^{-1}[\alpha,\bar\alpha]+\frac{3\sqrt{k}}{4}\hbar ca^{-1}[\beta,\bar\beta]\nonumber\\
		&-\frac{3\kappa^2}{4}a^3W^2+3\sqrt{k}a^2W+\frac{1}{2}a^3{W'}^2+\frac{3}{8}\hbar c\kappa^2W[\alpha,\bar\alpha]
		-\frac{3}{8}\hbar c\kappa^2W[\beta,\bar\beta]+\frac{\sqrt{3}}{2\sqrt{2}}\hbar c\kappa W'(\alpha\bar\beta-\bar\alpha\beta)
		+\frac{1}{2}\hbar cW''[\beta,\bar\beta]\nonumber\\
		&+\frac{3}{16}(\hbar c\kappa)^2a^{-3}\left(\bar\alpha\alpha\beta\bar\beta+\alpha\bar\alpha\bar\beta\beta\right).\label{Hquant}
	\end{align}
	\endgroup

The Hilbert space is generated from the vacuum state $\ket{1}$, which
satisfies\linebreak \mbox{$\alpha\ket{1}=\beta\ket{1}=0$}. Hence, there are four orthogonal states
\begin{equation}
	\ket{1},\quad\ket{2}=\bar{\alpha}\ket{1},\quad\ket{3}=\bar{\beta}\ket{1}\quad
	\mathrm{and}\quad\ket{4}=\bar{\alpha}\bar{\beta}\ket{1},\label{estados}
\end{equation}
which have norms $\braket{2|2}=\braket{1|1}$, $\braket{3|3}=-\braket{1|1}$ and
$\braket{4|4}=-\braket{1|1}$. Hence, a general state  has  the form
\begin{equation}
	\ket{\psi}=\psi_{1}(a,\phi)\ket{1}+\psi_{2}(a,\phi)\ket{2}+\psi_{3}(a,\phi)\ket{3}+\psi_{4}(a,\phi)\ket{4}.\label{estado}
\end{equation}

Therefore, from  constraint equation $S\ket{\psi}=0$, we obtain
\begin{align}
	a\left(\partial_{a}-\frac{3}{\hbar c} a^{2}W+\frac{6\sqrt{k}}{\hbar c\kappa^2}a+\frac{1}{2}a^{-1}\right)  \psi_{2}
	-\frac{\sqrt{6}}{\kappa}\left(  \partial_{\phi}-a^{3}W'\right)  \psi_{3}=0,\label{ec23}\\
	\left(  \partial_{a}-\frac{3}{\hbar c} a^{2}W+\frac{6\sqrt{k}}{\hbar c\kappa^{2}}a-a^{-1}\right)  \psi_{4}=0\quad \text{and}\quad
	\left(  \partial_{\phi}-\frac{1}{\hbar c}a^{3}W'\right)  \psi_{4}=0,\label{ec4}
\end{align}
while from $\bar{S}\psi=0$
\begin{align}
	a\left(\partial_{a}+\frac{3}{\hbar c} a^{2}W-\frac{6\sqrt{k}}{\hbar c\kappa^2}a+\frac{1}{2}a^{-1}\right)  \psi_{3}
	-\frac{\sqrt{6}}{\kappa}\left(  \partial_{\phi}+a^{3}W'\right)  \psi_{2}=0,\label{ec32}\\
	\left(  \partial_{a}+\frac{3}{\hbar c} a^{2}W-\frac{6\sqrt{k}}{\hbar c\kappa^{2}}a-a^{-1}\right)  \psi_{1}=0,\quad \text{and}\quad
	\left(  \partial_{\phi}+\frac{1}{\hbar c}a^{3}W'\right)  \psi_{1}=0,\label{ec1}
\end{align}

The terms with $a^{-1}$ in (\ref{ec23})--(\ref{ec1}) differ from those  in~\citep{previo:2016} due to a different operator ordering in the Hamiltonian. In fact, the classical Hamiltonian in~\citep{previo:2016} has a term $a^{-1}\pi_a^2$ that can be ordered in many ways to give a Hermitian operator as $a^{-1}\pi_a^2\rightarrow \frac{1}{2k+l}(ka^{-1}\pi_a^2+l\pi_a ^{-1} \pi_a+k\pi_aa^{-1})$.

\subsection{Solutions}\label{sec_sol}
As the Wheeler--DeWitt equation is second-order, its solutions require boundary conditions. However, in  supersymmetric theory, Equations (\ref{ec23})--(\ref{ec1})  are first-order and have unique solutions that can be fixed by consistency and normalization.
The equations for $\psi_{1}$ and $\psi_{4}$ can be straightforwardly solved yielding the unique solutions up to constant factors~\citep{tkachwf}
\begin{align}
	\psi_{1}(a,\phi) &  =A a\exp \left[-\frac{1}{\hbar c} \left( a^{3}W(\phi)-\frac{3\sqrt{k}a^{2}}{\kappa^{2}} \right) \right],\label{psi1aT}\\
	\psi_{4}(a,\phi) &  =A a\exp \left[\frac{1}{\hbar c} \left(  a^{3}W(\phi)-{\frac{3\sqrt{k}a^{2}}{\kappa^{2}}}\right)\right],\label{psi4aT}
\end{align}

The power of  factor $a$ of these solutions differs from the solutions in~\citep{previo:2016} due to the different operator ordering mentioned end of the preceding section. As shown in~\citep{previo:2016}, the solutions of  Equations (\ref{ec23}) and (\ref{ec32}) are not defined at $a=0$ unless they are trivial.
Thus, we chose the solutions
$\ket{\psi}=C_1\,\psi_{1}(a,\phi)\ket{1}+C_4\,\psi_{4}(a,\phi)\ket{4}$,
where $C_1$ and $C_4$ are arbitrary constants ~\citep{previo:2016}.
The norm of this state is
\begin{equation}
	\braket{\psi|\psi}=\left[|C_1|^2\int|\psi_1(a,\phi)|^2dad\phi-|C_4|^2\int|\psi_4(a,\phi)|^2dad\phi\right]\braket{1|1}.\label{norma}
\end{equation}

Classically, $a\geq0$ and could be a problem for quantization, e.g., it could require an infinite wall \cite{Isham}. However, solutions (\ref{psi1aT}) and (\ref{psi4aT}) already vanish at $a=0$. For a positive superpotential, $\psi_{1}$ has a bell form and tends to zero as $a$ increases; see Figure \ref{fig_campana}. In this case,  solution $\psi_{2}$ must be set to be the trivial one. Oppositely, for a negative superpotential, $\psi_{2}$ tends to zero as $a$ increases, and $\psi_{1}$ must be discarded.
For $\phi\to\pm\infty$, the behavior of  (\ref{psi1aT}) and (\ref{psi4aT}) depends on the form of the superpotential.
Therefore, we considered only positive or negative superpotentials, and we chose $\braket{1|1}=1$ for positive superpotentials, and $\braket{1|1}=-1$ for negative superpotentials. Hence,
\begin{align}
	\ket{\psi}  &  = C\psi_1(a,\phi)\ket{1},\quad\text{if}\ W(\phi)>0,\label{psi1w}\\
	\ket{\psi}  &  =C\psi_4(a,\phi)\ket{4},\quad\text{if}\ W(\phi)<0. \label{psi4w}
\end{align}

From Expansions (\ref{estado}), and (\ref{estados}), we see that these states correspond to scalars. By construction, these states are invariant under supersymmetry transformations.

\begin{figure}[h!]
	\includegraphics[height=4cm,width=6cm]{Campana.pdf}
	\caption{Profile of $\psi^2(a,\phi)$, for $\phi$ constant.}
	\label{fig_campana}
\end{figure}

Further, for $\phi\to\pm\infty$, the behavior of (\ref{psi1aT}) and (\ref{psi4aT}) depends on the form of the superpotential. For a localized particle, the wave function has well-defined position probabilities and probability conservation. These conditions also guarantee hermicity of operators. On the other side,  the wave functions of free particles do not vanish at infinity, but can be given a meaning by considering relative probabilities. If we restrict the superpotential to be an even function of $\phi$, then operators $\pi_\phi$ and $H_0$ are self-adjoint even if the wave function does not vanish at $\phi\to\pm\infty$. Otherwise, if the wave function vanishes at $\phi\to0$, the domain of $\phi$ can be taken to be $[0,\infty)$. A self-adjoint Hamiltonian constraint is consistent with the lack of evolution in the Heisenberg picture
\begin{equation}
	\bra{\psi}\frac{da}{dt}\ket{\psi}=\frac{i}{\hbar}\bra{\psi}[H_0,a]\ket{\psi}=0.\label{noevol}
\end{equation}

In the following, unless otherwise stated, we consider $k=0$. In this case, we can write either (\ref{psi1w}) or (\ref{psi4w}) as
\begin{align}
	\psi(a,\phi)  = Ca\exp \left[-\frac{1}{\hbar c} a^{3}|W(\phi)| \right]. \label{psiw}
\end{align}

This wave function differs from the one in~\citep{previo:2016}, by the power of the $a$ in front of the exponential, due to a different operator ordering, as mentioned in the preceding section.

In  Appendix~\ref{appa} we give the expressions for $k=1$.

\section{Time}
\label{time}
Ordinary quantum mechanics assigns operators with real spectra to observables and probability amplitudes for their occurrence. A time dependence of the wave function is generated by the Hamiltonian operator. However, in an actually occurring state, a definite time entails certain energy indeterminacy. Hence, the energy spectrum cannot be restricted to one value, and time-dependent mean values arise by interference among different energy states. In general relativity, the Hamiltonian is constrained to vanish, and time is undetermined. This is consistent, since different energy states can manifest only if there is an environment that makes possible transitions among them. Nonetheless, the universe certainly has different components interacting at least gravitationally, and one such component, suitable chosen, can play the role of a clock~\citep{banks}; see also~\citep{Kuchar,Anderson}.

In~\citep{previo:2016}, we chose the scalar field as time parameter, and defined an effective time-dependent wave function that allows for computing time-dependent mean values. Here, we analyze  Wave Function (\ref{psiw}) and its probability density regarding the motivation of this choice of time.

We adopted the standard interpretation of quantum mechanics for the solutions of the Wheeler--DeWitt equation. Hence, the square modulus of the wave function gives the probability density for the possible three-geometries. Further, invariance under time reparametrizations ensures that the superspaces of each of the space slices are equivalent. Thus, this wave function describes, in  a quantum mechanical sense, the space geometries of the whole spacetime.
Furthermore, if it is possible to identify mean trajectories in superspace along regions around the maxima of the wave function, then it should be possible to parametrize these trajectories following the idea of Misner's supertime~\citep{misner}. These trajectories should be around classical trajectories~\citep{halliwell} corresponding to effective theories. Strictly speaking, measurements should give random values around these mean values.

In the model of this paper, the configuration space is given by the scale factor and the scalar field. Further, from  (\ref{psiw}), we see that, if we keep $\phi$ constant, the probability density of Wave Function (\ref{psiw}) has the generic bell form of Figure \ref{fig_campana}, with the maximum at
\begin{equation}
	a_{\text{max}}(\phi)=\left[\frac{\hbar c}{3W(\phi)}\right]^{1/3}.\label{amax}
\end{equation}

Allowing  for $\phi$ to vary, these maxima trace out a curve of most probable values of the scale factor. The probability density along this curve is
\begin{equation}
	\psi^2(a_{\text{max}},\phi)=e^{-2/3} a^2_{\text{max}}(\phi),
\end{equation}

Therefore, higher values of the scale factor along this curve have a higher relative probability, and we could think of an expanding universe for this wave function. On the other side, in quantum mechanics mean values are  generally time-dependent, and we can speculate that later times correspond   to higher probabilities here. Hence, time would increase monotonically with the scale factor. Nevertheless, $a_{\text{max}}$ is driven by Scalar Field (\ref{amax}); hence, a natural choice for time is the scalar field, and the superpotential should ensure that $a_{\text{max}}$ increases properly. Such a choice corresponds to a gauge where the scalar field is constant on the spacial slices. In this case, the universe is not localized in the $\phi$ direction and the wave function is not normalizable in this direction, but relative probabilities can be considered, i.e., quotients of probabilities. As the value of $\phi$ is highly uncertain, a measurement gives random values, and we can ask then for the probability that the scale factor takes a value, which is given by the conditional probability of obtaining this value of $a$, given a value of $\phi$ ~\citep{previo:2016}
\begin{equation}
	\left\vert\Psi(a,\phi)\right\vert^2=\frac{\left\vert\psi(a,\phi)\right\vert^2}{\int_0^\infty da\,\vert\psi(a,\phi)\vert^2}.\label{condprob}
\end{equation}

This probability must be used if there is a correlation between both fields, as required for a clock in~\citep{banks}, where it is called relative probability.
Probability (\ref{condprob}) can be obtained~\citep{previo:2016} from a wave function normalized for a given value of $\phi$
\begin{equation}
	\Psi(a,\phi)=\frac{1}{\sqrt{\int_0^\infty da\,\vert\psi(a,\phi)\vert^2}}\,\psi(a,\phi).
	\label{onda}
\end{equation}

Thus, making $\kappa\phi\to t/\mu$  where $\mu$ accounts for the time scale, \protect and taking Solution~(\ref{psiw}), Wave Function (\ref{onda}) becomes
\begin{equation}
	\Psi(a,t)=\sqrt{\frac{6|W(t)|}{\hbar c}}a\exp\left[{-\frac{a^{3}|W(t)|}{\hbar c}}\right],
	\label{ondaw}
\end{equation}
and satisfies a conservation equation~\citep{previo:2016}. Further, as the observed universe is classical, what we can give a meaning to, following the Ehrenfest theorem, is mean values. Thus, under the preceding ansatz, for the scale factor, we obtain~\citep{previo:2016}
\begin{equation}
	a(t)=\int_0^\infty a|\Psi(a,t)|^2 da=\Gamma\left(4/3\right)\left[\frac{\hbar c}{2|W(t)|}\right]^{1/3}, \label{amean}
\end{equation}
which is close to (\ref{amax}), as their quotient is $\Gamma(4/3)(3/2)^{1/3}\sim1.02$.

The quantum fluctuations produce standard deviations  that satisfy the Heisenberg relation~\citep{previo:2016}.

In this work, we are not producing any approximation, semiclassical or of another type. As the fermionic degrees of freedom do not have classical counterparts, the mean values do not necessarily correspond to trajectories that approximate classical solutions, see e.g.,~\citep{obregon2}.  Actually, (\ref{amean}) can be inserted into the Friedmann equations, from which a potential can be read out. {\protect If we consider the effective FLRW model with a scalar, obtained by inserting~(\ref{amean}) into the Friedmann equations, the corresponding potential can be read out as a time~function}
\begin{equation}
	\frac{1}{3c^4\kappa^2}\left(\frac{2{W'}^{2}}{W^2}-\frac{W''}{W}\right),
\end{equation}
which can be compared with the scalar potential (\ref{scalarpot}),  which follows when the fermionic terms in the Hamiltonian are eliminated.

The results for this section can also be given analytically  for $k=1$; see Appendix~\ref{appa}. They involve hypergeometric, AiryBi, and AiryBi$'$ functions that have exponential behavior, and their numerical evaluation is troublesome. As we were  interested in qualitative features here, we restricted ourselves to $k=0$. In this case, considering that the sign of the superpotential did not have consequences for the wave function or the scalar potential, we chose the superpotential as positive definite in the following.

\section{Inflationary Model}
\label{inflation}
In this section, we consider a class of phenomenological superpotentials that give inflationary dynamics that satisfactorily agrees  with the observational bounds. Potentials of this form appear, e.g., in string-inspired tachyon models. With these superpotentials, the wave function tends to zero as $\phi\to 0$, and we can restrict $\phi\geq0$, as mentioned in Section \ref{sec_sol}. Thus, we consider universes with origin at $t=0$, described by homogeneous quantum cosmology from its very beginning, although above Planck scale, full gravitational interactions become relevant, and some ultraviolet completion would be required.

In~\citep{previo3}, we performed a qualitative discussion of several superpotentials that have diverse drawbacks, as phantom matter. Here, we consider a family of superpotentials
\begin{equation}\label{superp}
	W(\phi)=\frac{c^4 M_p^3}{\hbar^2}\left[\frac{\sqrt{8\pi}\ \Gamma(4/3)}{2^{1/3}n}\right]^{1/3} \left\{\frac{(\kappa\phi)^{-p}}{\left[1 + e^{(\kappa\phi)^{1/2}}\right]}+ \lambda\right\},
\end{equation}
for $p>0$. The wave function fulfils $\lim_{a\to0}\psi(a,\phi)=0$ and  $\lim_{\phi\to0}\psi(a,\phi)=0$.

Thus, from (\ref{amean}), we have
\begin{equation}\label{at}
	a(t)=n\ell_P\left[\frac{t^p\left(1+e^{\sqrt{t/\mu}}\right)}{\mu^p+\lambda t^p\left(1+e^{\sqrt{t/\mu}}\right)}\right]^{1/3},
\end{equation}
where $\ell_P$ is the Planck length. In the following, we set the normalization constant equal to one, $n=1$, and we redefined the scale factor to be dimensionless, $a/\ell_P\to a$. Constant $\mu$ accounts for the time scale.
With respect to $\lambda$,  (\ref{amean}) shows  that, if the value of $W$ decreases, the scale factor  grows, and, in order to finish this growth, $W$ must stop  decreasing; this is the role of $\lambda$, which must be positive. Thus, in order to have a sufficiently large increase in  scale factor, $\lambda$ must be small enough. This parameter could be seen as the remainder of a term responsible for dark energy in the superpotential
\begin{equation}
	\frac{\lambda}{1+e^{\beta(\phi-\phi_d)}},
\end{equation}
we do not pursue  this idea further in this work.

For the verification of the predictions of the evolution of Scale Factor (\ref{at}), we consider $N=60$ $e$ folds and observational data of PLANCK observatory~
\begin{itemize}
	\item  Tensor-to-scalar ratio bound $r<0.032$, \citep{tristram},

	\item  Scalar spectral index $n_s=0.9649\pm 0.0042$, \citep{planck}.
\end{itemize}

The acceleration, as usual, can be written by  identity
\begin{equation}
	\ddot{a}(t)=a H^2(t)(1-\varepsilon(t)),
\end{equation}
where $\varepsilon(t)=-\frac{\dot{H}(t)}{H^2(t)}$ is the slow-roll parameter.

The enhancing effect of inflation on inhomogeneous quantum fluctuations is well-known~\citep{baumann}. As a consequence, the fluctuations last after inflation and produce structure seeds, and gravitational waves are generated in the process. These primordial effects last in the CMB, and their study led to stringent bounds on virtual predictions of inflationary models, such as the tensor-to-scalar ratio $r$ and  scalar spectral index $n_s$, that can be evaluated directly from the characteristics of the inflationary evolution.

The tensor-to-scalar ratio is the quotient of the tensor-to-scalar power spectra and is given by
\begin{equation}
	r=16\varepsilon(t).\label{r}
\end{equation}

Scalar spectral index $n_s$ follows from   scalar power spectrum
\begin{equation}
	{\Delta_s}^2(t)=\left.\frac{1}{8\pi^2{M_P}^2}\frac{H^2(t)}{\varepsilon(t)}\right|_{a(t)H(t)=k},
\end{equation}
as
\begin{equation}\label{ns}
	n_s(t)=1+\left.\frac{d\ln {\Delta_s(t)}^2}{d\ln k}\right|_{a(t)H(t)=k},
\end{equation}
where $k$ are the wavenumbers of the scalar perturbations that, during inflation, exit the horizon at time $t$, i.e., $a(t)H(t)=\dot{a}(t)=k$. Thus, (\ref{ns}) can be written as
\begin{equation}
	n_s(t)=1+\left.k\frac{dt}{dk}\frac{d\ln{\Delta_s(t)}^2}{dt}\right|_{a(t)H(t)=k}=1+\left.\frac{\dot{a}(t)}{\ddot{a}(t)}
	\frac{d\ln{\Delta_s(t)}^2}{dt}\right|_{a(t)H(t)=k}.
\end{equation}
which can also be written  in terms of the Hubble parameter
\begin{equation}
	n_s=\frac{\dot{H}(H^2+5\dot{H})-H\ddot{H}}{\dot{H}(H^2+\dot{H})}.
\end{equation}

Therefore, in order to estimate the values of $r$ and $n_s$ predicted by our model during inflation, we can evaluate them in the dependence of time.

A first approximation for $\lambda$ can be obtained from the limit of very large times of the scale factor, $\lim_{t\to\infty}a(t)=1/\lambda\sim e^N$. $N$ are the $e$ folds generated by inflation for the scale~factor
\begin{equation}\label{efolds}
	e^N=\frac{a(t_{\text{exit}})}{a(t_{\text{in}})},
\end{equation}
where $t_{\text{in}}$ and $t_{\text{exit}}$ are  the beginning and end times of inflation.
Then, if we compute (\ref{efolds}) with the scale factor (\ref{at}), we can solve for $\lambda$
\begin{equation}\label{lambda1}
	\lambda=\frac{\mu^p}{e^{3 N}-1}\left[\frac{1}{{t_{\text{in}}}^p\left(1+e^{\sqrt{t_{\text{in}}/\mu}}\right)}-\frac{e^{3N}}{{t_{\text{exit}}}^p\left(1+e^{\sqrt{t_{\text{exit}}/\mu}}\right)}
	\right]
\end{equation}

Further, as $\lambda>0$, from (\ref{lambda1}) we obtain a condition for $\mu$. For instance, as $t_{\text{in}}\ll t_{\text{exit}}$, if we set $t_{\text{in}}\ll \mu\ll t_{\text{exit}}$, we can approximate $e^{t_{\text{in}}/\mu}\ll 1$ and $e^{t_{\text{exit}}/\mu}\gg 1$. In this case,
\begin{equation}\label{mu}
	\mu<\frac{t_{\text{exit}}}{[3N+p(\ln t_{\text{in}}-\ln t_{\text{exit}})]^2}.
\end{equation}

Strictly speaking, we must still define how to define the entry and exit times of inflation depending on the evolution of the scale factor. Relations (\ref{lambda1}) and (\ref{mu}) help in checking the consistency for choices of $\mu$ and $\lambda$. With this in mind, we can fix the values of these parameters and evaluate the behavior in each case.

In order to get criteria for the entry and exit times, we first analyse the limits of the scale factor, its velocity, and acceleration as $t\to0$.  It turns out as follows. The scale factor tends zero for $p>0$. The velocity tends to $\infty$ for $0<p<3$, for $p=3$ it tends to $\frac{2^{1/3}}{\mu}$, and for $p>3$ it tends to zero. The acceleration tends to $-\infty$ for $0< p<3$, for $3\leq p<6$ it tends to $\infty$, for $p=6$ it tends to $\frac{2^{4/3}}{\mu^2}$, and for $p>6$ it is zero. Additionally, for $t\to\infty$, the scale factor tends to $1/\lambda$, the velocity tends to $0^{+}$, and the acceleration tends to $0^{-}$.

Considering now the acceleration, if it is negative at $t=0$, for $0<p<3$, it increases until it becomes zero and then positive; we took this zero as the entry time for inflation, see Figure \ref{fig_entry}. Further, the acceleration continues increasing until a maximum later, and after that becomes zero again, and then negative. We took this second zero as the exit time. Afterwards, the acceleration has a minimum, and then tends to zero from the negative numbers; see Figure \ref{fig_exit}. For  cases $3\leq p<6$ where the acceleration tends to infinity at $t=0$, it decreases to a very small minimum that can be taken as the entry time, see Figure \ref{fig_entry}. Further, as in the previous case, it has a maximum and then a zero, and we took it as exit time. For $p\geq 6$, the acceleration at $t=0$ is equal to or larger than zero and increases from the beginning; hence, the entry time is zero, and, as $a(0)=0$, there is no precise way to give an initial time for inflation. For this reason, we considered only $0\leq p<5$.

Further, as a first input, we took the initial time for inflation at a scale lower than the GUT scale  $10^{15}$ GeV. Hence, $t_{\text{in}}\gtrsim 5\times 10^6$~T\textsubscript{P} $\approx 10^{-37}$ s. For the exit of inflation, we took the generally accepted interval $t\sim10^{-33}$--$10^{-32}$ s, and we set  $t_{R}=5\times 10^{-33}$ s = $3.7\times 10^{10}$~T\textsubscript{P}, as reference time for  exit $t_{\text{exit}}\approx t_R$. With these times, for a given value of $p$, we   estimated from (\ref{mu}) and set  $\mu\sim\times 10^6$ T\textsubscript{P}. From it, we computed $\lambda$ from (\ref{lambda1}) for $N=60$, and then evaluated  the entry and exit times from the acceleration $\ddot{a}(t)$. Following this procedure, we adjusted $\mu$ and $\lambda$, so that $t_{\text{exit}}\approx t_R$ and $N=\ln a(t_{\text{exit}})/a(t_{\text{in}})\approx 60$. With these data, we computed the tensor to scalar ratio (\ref{r}), and the scalar spectral index (\ref{ns}). We performed these steps for $p=1,2,3,4,5$.
\begin{figure}[h!]
	\includegraphics[width=13cm]{entry.png}
	\caption{Inflation  entry times for $p=2$ and $p=3$.}
	\label{fig_entry}
\end{figure}

\begin{figure}[h!]
	\includegraphics[width=7cm]{Exit.pdf}
	\caption{Inflation exit time for $p=1$.}
	\label{fig_exit}
\end{figure}

It is remarkable that, with the parameters fixed in the previous way, for given \mbox{$0<p\leq 5$}, the entry time is of the order of $10^6$ T\textsubscript{P}, and   the tensor/scalar ratio and the scalar spectral index agree quite well with the observational constrains.

Tensor/scalar Ratio (\ref{r}) (see Figure \ref{fig_r}) satisfies    bound $r<0.032$ \citep{tristram} very well and depends slightly on $p$.
\begin{figure}[h!]
	\includegraphics[width=7cm]{r.png}
	\caption{Tensor/scalar ratio.}
	\label{fig_r}
\end{figure}

\noindent

Further, from (\ref{ns}), we computed the scalar spectral index whose behavior is shown in Figure \ref{fig_ns}.
\begin{figure}[h!]
	\includegraphics[width=7cm]{ns.png}
	\caption{Scalar spectral index.}
	\label{fig_ns}
\end{figure}

Here, the agreement with  observational bound $0.9649 \pm 0.0042$ (with $68\%$ CL)~\citep{planck}, was very good for most of the duration of inflation, as shown in Figure \ref{fig_ns2}. It is also  slightly dependent of $p$. Note that the running of the scalar spectral index $\frac{d n_s}{d \ln k}$ is positive, with a value around $0.0004$, with a a negative running of running.
\begin{figure}[h!]

	\includegraphics[width=7cm]{ns2.png}
	\caption{Detail of scalar spectral index.}
	\label{fig_ns2}
\end{figure}
\section{Discussion}
\label{discussion}

\textls[-25]{Quantum cosmology gives a canonical quantization of general relativity in the Schr\"odinger picture, }with the Wheeler--DeWitt equation as  a time-independent Schr\"odinger equation. The wave function gives the probability amplitudes for the occurrence of all possible spatial three-geometries and field distributions, at any time. On the other hand, the observed universe is classical and has time, and classical physics follows from quantum physics, hence an effective time evolution should follow from the quantum description. Further, the Wheeler--DeWitt equation is a second-order scalar equation. In the supersymmetric case, there is a system of first-order equations whose solutions are spinorial wave functions, see, e.g.,~\citep{eath,moniz-1}. A particular meaning of the components of these wave functions has not been given; it would quickly lead to a Machian discussion. In many cases, there are only two nonvanishing components, see, e.g.,~\citep{obregon1}, given by real exponentials with opposite exponent sign.
Here, we considered an FLRW theory with a minimally coupled scalar field. Single-field models are extremely effective to account for the inflationary~era.

From the four components of the solution of the supersymmetric Wheeler--DeWitt equation, only one tends to zero as $a\to\infty$, and the other can be taken to be trivial. The form of Solution (\ref{psiw}) suggests the ansatz that, in a certain gauge, time can be given by the scalar field, and trajectories for the observables are mean values on an effective wave function that corresponds to conditional probabilities. Thus, for the scale factor, we obtain an evolution $a(t)$, and we can perform time reparametrizations considering that it is scalar $a'(t')=a(t)$. The resulting evolution is nonperturbative. These trajectories are classical if the quantum fluctuations are negligible. The time proposed here does not follow from a semiclassical approach.

We  considered in this formulation {\protect one  family of inflationary models that depends on the parameter $p>0$; as for $p>5$ there is eternal inflation, we restrict it to $p<5$ and for simplicity consider only integer values. There are other two parameters,  $\mu$ and $\lambda$; the first  fixes the time scale. Parameter $\lambda$ corresponds to the extent of the inflation, the $e$ folds. We convened to set the entry of inflation, depending on the value of $p$, at zeros or minima of the acceleration, and exit times as zeros. In this way, for all $p$, we adjusted parameters $\mu$ and $\lambda$, so that the exit time coincided with a reference time $t_R=5\times 10^{-33} s$, and $N\approx 60$. With this setting, the corresponding tensor-to-scalar ratio and scalar spectral index can be computed with values that agree with the observational bounds remarkably well}.

For indepth analysis, inhomogeneous perturbations should be introduced to evaluate their evolution and the the production of primordial gravitational waves. These computations should be performed at best in the superfield formalism. An interesting perspective is also the study of this formalism for dark energy.

\vskip 1truecm

\centerline{\bf Acknowledgements}
C.R. thanks O. Obreg\'on and H. Garc\'{\i}a-Compe\'an, and  V. V.  thanks G. Garc\'{\i}a-Arroyo and J.A. V\'azquez
for the interesting discussions. This research was funded by VIEP-BUAP. N.E. Martínez-
Pérez thanks CONACyT for studies grant.
conflict of interest.

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There are "unlikely" to be any survivors on board the AN-32 aircraft that went missing over the Bay of Bengal on July 22, the government said in Lok Sabha on Friday.
Minister of state for defence Subhash Ramrao Bhamre said during Question Hour that it is "unlikely" that there are any survivors after so many days of the incident.
He was responding to a question by deputy speaker M Thambi Durai, also an AIADMK member, who insisted that the search for the missing transport aircraft will not stop till its wreckage is found. The minister said a variety of aircraft, including helicopters of the air force and coast guard, have been pressed into service to locate the plane.
Merchant vessels and the fishermen community have also been requested to look out for debris.
30 floating objects were located but no "concrete" evidence has yet been found.
Bhambre said the complete wreckage of Malaysian Airlines flight MH 370, which had disappeared on March 8, 2014, has not been found so far, while the wreckage of a French airliner was found over a year after it had gone missing, he said explaining the difficulties in finding the missing planes.
The wreckage and remains of the crew of a Coast Guard Dornier aircraft was also found after several days, he said.
He said on the fateful day, the radars tracking the aircraft had found a "thunder cloud bad patch" but the plane was equipped with the device to avoid such a disturbance.
The ill-fated AN-32 had taken off on a routine courier flight to Port Blair from Tambaram air base near Chennai on July 22 at 8.30 am with six crew and 23 personnel, but never arrived at the destination. It was last seen on the radars at 9 AM.


text:
Itamar ( אִיתָמָר, podle biblického kněze Ítamara, v oficiálním přepisu do angličtiny Itamar) je izraelská osada a vesnice typu společná osada (jišuv kehilati) na Západním břehu Jordánu v distriktu Judea a Samaří a v Oblastní radě Šomron (Samařsko).

Geografie
Nachází se v nadmořské výšce 660 metrů v centrální hornaté části Samařska, cca 6 km jihovýchodně od města Nábulus, cca 15 km severovýchodně od města Ariel, cca 45 km severoseverovýchodně od historického jádra Jeruzaléma a cca 50 km severovýchodně od centra Tel Avivu.

Na dopravní síť Západního břehu Jordánu je napojena pomocí lokálních silnic, které se pak napojují na dálnici číslo 60, která vede severojižním směrem napříč téměř celým regionem Samařska a propojuje Jeruzalém s městem Nábulus.

Jde o izolovanou izraelskou osadu situovanou hluboko do vnitrozemí Západního břehu Jordánu a obklopenou četnými palestinskými vesnicemi a městy (Rudžejb na západě, Awarta na jihu a Bajt Furik na severovýchodě). Pouze na jihovýchodní straně přechází území osady Itamar do prakticky neobydlené polopouštní krajiny, na svazích nad okrajem Jordánského údolí. Nejbližší izraelskou osadou je Har Bracha asi 4 km severozápadním směrem a Elon More asi 7 km na severovýchod.

Dějiny
Obec Itamar vznikla v roce 1984. Prvními usedlíky byla skupina několika rodin okolo ješivy Machon Me'ir z Jeruzaléma. Původní název osady zněl Tel Chajim (podle Chajima Landaua, jednoho z velitelů vojenské irganizace Irgun a pozdějšího ministra izraelských vlád). Zpočátku sestávala osada ze dvou řad prefabrikovaných betonových domů. V osadě nebyla zavedena elektřina a proud dodával generátor. V domech chyběly telefonní linky. Počátkem 90. let byl na okraji vsi vysázen les s více než 30 tisíci stromy.

Od 2. poloviny 90. let 20. století vzniklo okolo vlastního Itamaru několik satelitních skupin domů, zejména jihovýchodním směrem. V roce 1996 to byla lokalita ha-Nekuda, v roce 1998 skupiny domů Kóta 851, Kóta 782, Kóta 836 a Gv'aot Olam,v roce 1999 byla osídlena Kóta 777. Podle údajů z roku 2007 žilo v těchto satelitních čtvrtích celkem 116 stálých obyvatel (nejvíce na Kótě 851). Další lokality byly sice stavebně využity, ale bez trvalého osídlení, jako třeba lokalita Itamar-sever, která sestávala jen z jednoho prázdného kovového kontejneru. Vznik mnoha z těchto satelitních lokalit obklopujících vlastní Itamar inicioval místní aktivista Avri Ran. Ten založil v roce 1998 i lokalitu Gv'aot Olam, kde se pak usadil a zřídil zde privátní ranč a organickou biofarmu. Žije na ní se svou početnou rodinou a rodinami svých dětí. Výrobky z farmy se objevují v maloobchodní síti v celém Izraeli.

Počátkem 21. století nebyl Itamar pro izolovanou polohu zahrnut do Izraelské bezpečnostní bariéry, která odděluje některé bloky izraelských osad od oblastí osídlených Palestinci. Budoucí existence obce je závislá na podmínkách případné mírové smlouvy mezi Izraelem a Palestinci.

Vzhledem k poloze hluboko ve vnitrozemí Západního břehu Jordánu byla vesnice opakovaně terčem palestinských útoků. 8. května 2001 byl zavražděn Arnaldo Agranionic, který působil jako strážce izolované farmy Chavat Binjamin, jež se nacházela na jednom z vrcholků východně od vlastní osady. 27. srpna 2001 zemřel při přepadení Me'ir Lixenberg, obyvatel Itamaru, když byl přepaden při jízdě na silnici mezi osadou Har Bracha a Itamar. 28. května 2002 pronikl do Itamaru palestinský ozbrojenec a zavraždil tři lidi předtím, než byl sám zabit. K akci se přihlásily Brigády mučedníků Al-Aksá. Infiltrace osady palestinským útočníkem se opakovala 20. června 2002. Zemřela tehdy čtyřicetiletá žena a tři její synové a dále její soused, který přišel napadené rodině na pomoc. Útočník pak byl zabit. K útoku se přihlásily Brigády mučedníků Al-Aksá a Lidová fronta pro osvobození Palestiny. V srpnu 2004 byl zabit jeden obyvatel Itamaru, když na něj před vjezdem do vesnice zahájil střelbu palestinský útočník. K akci se přihlásily Brigády mučedníků Al-Aksá. V noci 11. března 2011 pronikli do Itamaru dva palestinští teroristé. Ubodali manželský pár Fogelových a jejich tři děti včetně tříměsíčního kojence. Rok po vraždách byla slavnostně otevřena nová budova ješivy pojmenovaná Miškan Ehud podle zavražděného otce rodiny.

Demografie
Obyvatelstvo v obci Itamar je v databázi rady Ješa popisováno jako převážně složené z nábožensky orientovaných Izraelců. Podle údajů z roku 2014 tvořili naprostou většinu obyvatel Židé (včetně statistické kategorie "ostatní", která zahrnuje nearabské obyvatele židovského původu ale bez formální příslušnosti k židovskému náboženství).

Jde o menší obec vesnického typu s dlouhodobě rostoucí populací. K 31. prosinci 2014 zde žilo 1275 lidí. Během roku 2014 registrovaná populace stoupla o 24,3 %.

Odkazy

Reference

Související články
 Samařsko
 Izraelská bezpečnostní bariéra
 Oblastní rada Šomron

Externí odkazy

 Oficiální profil obce na portálu Oblastní rady Šomron
  Fotografie obce

Izraelské osady na Západním břehu Jordánu
Oblastní rada Šomron
Společné osady na Západním břehu Jordánu
Sídla nábožensko-sionistické komunity

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Marking the start of groundworks for Newark's new fire station are (centre, with spade) the chairman of Nottinghamshire Fire Authority, Brian Grocock, and (right) Newark station officer Seth Armstrong. They are with (left to right) Nottinghamshire Fire and Rescue Service head of procurement and resources Ian Pritchard; Major Contracts director for Gelder Group, Kevin Manterfield-Ivory; site manager Ian Keogh and contracts manager Gavin Parker.
Newark Fire and Rescue Station will start to take shape now all demolition works have been completed. A traditional sod cutting ceremony took place last week to mark the next phase of the project.
The ceremony was attended by Kevin Manterfield, Gavin Parker and Ian Keogh along with the chairman of Nottinghamshire Fire Authority, Brian Grocock, and Newark station officer Seth Armstrong.


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#WeAreAlSharqi
What Do You Want To Ship
World Shipping Routes
Our Philosophy Our motto "Helping you grow" forms an important part of our work DNA
HOW IT ALL STARTED –
Al Sharqi Shipping was first founded by Mr. Muhammad Rafiq in the year 1989. After spending nearly a decade in the Shipping and Logistics Industry of Dubai, Mr. Rafiq forayed into his own vision of what he thought the industry needed – a better experience for all the stakeholders involved.
At the time, the industry was plagued with unprofessionalism, defaults on commitments and a depressed customer supply chain; dishonesty was widespread. It was during this time, Mr. Rafiq decided to provide an alternative to the customer: a company that is built on solid value and committed not only to its service but to all of its stakeholders as well.
Al Sharqi Shipping wanted to "Help You Grow"
Today, "helping you grow" has formed an important part of our business philosophy and mindset. A mindset which helped us grow from a handful of customers to becoming one of the major players in the region.
HELP SHIPPER GROW
You, as the shipper, are one of the key players in the industry. And we, at Al Sharqi, want to help you grow. Our aim is to provide the best possible service to our customers, the shippers. We want to help our customers grow, to achieve their goals.
By use of technology, smart people and a strong commitment to our values, we adapt and deliver to our customer's needs for timely supply chain solutions – offering them visibility and insights. In fact, our customers who have been with us for the last 20-25 years appreciate the honesty and transparency in our practices, the attention to details in our interactions and our promise to deliver on their commitments.
HELP CARRIER GROW
About 90% of world trade is carried by the international shipping industry and air cargo alone carried 51.2 million tons of freight in 2015 and 35% of interregional exports of goods by value.
Carriers are an important pillar to Global Trade and to our Shipping Ecosystems. It is with the support of these carriers that we are able to fulfill our commitments – whether it's a one-time load or a dedicated trade lane. We care about building a strong, long-lasting relationship with our partners and that is why we are committed to our carriers growth as well.Our round the clock helpline is not just available to our customers, but also to our partners. Our aim is to collaborate with them and help them make their process smoother, so we can mutually grow together.
Read more about our continuous collaboration and achievements with our partners, the carriers.
HELP EACH OTHER GROW
As a family run business, each member of Al Sharqi is part of the family. For us at Al Sharqi, a family is not just a term, but rather a commitment to each other. Whether you are located at our branch in Tanzania, Pakistan or UAE, you are part of the Al Sharqi family. Top to down, horizontally or vertically, we share in each other's success. At Al Sharqi, everyone matters. We take care of each other and we help each other grow. Our hiring practices are not just looking for a good fit with the organization, but rather with the family as well – people who are willing to learn and grow every day. These deeply ingrained values are what drives our organizational culture and performance. It's simple: at Al Sharqi, you'll have the opportunity to not only grow professionally but also personally.
HELP COMMUNITIES GROW
Al Sharqi Shipping is continuously looking for ways to help out the community. Each member of the Al Sharqi family is embedded with a deep sense of respect for our community and its needs. Whether its meal box distribution during Ramadan season or our year-round proud support of the Rashed Center for Disabled, Al Sharqi has its hands and feet planted firmly in the community. Local or international, the Al Sharqi family is looking to increase its community footprint and is always striving to give back.
If you have an initiative which requires Al Sharqi's support, we are all ears. Reach out to us here.
Al Sharqi wants to help our community grow.
HELP ENVIRONMENT GROW
As a strong believer and implementer of corporate social responsibility, Al Sharqi has tuned its business practices around the same principles. Continuously seeking to reduce its carbon footprint on the environment, Al Sharqi is always looking ways to streamline its processes, eliminate inefficiencies and reduce waste. From introducing concepts such as "zero waste paper" or Driver's education to reduce the amount of Co2 emissions in our daily operations, we are constantly working to not only reduce our impact on the environment but to also benefit it.
Let Al Sharqi help you grow.
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Indigenous Social Entrepreneurship Event Opening Address - Speech, Canberra
Posted by Andrew Leigh 56sc on June 05, 2019
INDIGENOUS SOCIAL ENTREPRENEURSHIP EVENT
Like Auntie Roslyn Brown, I acknowledge that we're meeting on traditional lands of the Ngunnawal people and pay my respect to elders, past and present. I acknowledge the extraordinary leadership of Cindy Mitchell as the executive chief executive officer of Mill House Ventures, recognise Maree Sainsbury, Peter Radoll, Dennis Foley, Susan Moylan-Coombs, Adrian Appo and many other distinguished guests here today. I was a regular visitor to University of Canberra's campus during the course of the election campaign and I certainly hope to be back on a regular basis over the course of this term, and I'll say very briefly at the end of some remarks about one of those visits.
When I was at university, I worked as an instructor at Sport and Recreation camps. One of the things we used to teach children to do was to throw a boomerang. One of the great things you can do when you've got a group of kids around and they're looking at a boomerang is to turn the boomerang over so the flat side is up and ask them to tell you the difference between the two arms of the boomerang. Eventually they see the bevelled edge of the two arms sits on the bottom of one arm on the top of the other. When they reflect on it a bit more they realise that it's those two bevels that cause the boomerang as it spins to trace out an arc. In an instant they come to realise the sheer ingenuity of those who tens of thousands of years ago invented the boomerang.
Indigenous Australians also invented the Woomera, a spear throwing device which allows spears to go three times as fast as if they're thrown by hand and to embed themselves with terrifying speed into a tree or an animal. They invented fire stick farming and water bags. White settlers thought they were being very clever when they come and came up with the Coolgardie safe, but really they were just putting into practice the evaporative technologies that Indigenous Australians had known about for tens of thousands of years.
In the 17th century Galileo was asked whether he thought there was a relationship between the movements of the moon and the tides. He said no, they were unrelated. Unfortunately he should have consulted the Yolngu people, who had known for tens of thousands of years before that that the moon and the tides were intertwined. Aboriginal people had been using the stars to navigate before white sailors set about doing the same thing. And if you happen to have a $50 note in your pocket, you'll see that it depicts David Unaipon. David Unaipon is known as the Australian Leonardo da Vinci, somebody who in the course of his lifetime put in place nineteen provisional patents. Those included mechanical sheep shears and a centrifugal motion machine. He was ahead of his time, but of course faced considerable racism and so wasn't able to get the final patents and the due credit during his lifetime for his extraordinary ingenuity.
Knowing all of this, and understanding University of Canberra's extraordinary commitment to Indigenous engagement, we made a commitment during to assist Indigenous entrepreneurship programs here at the University of Canberra. We did so knowing that the University of Canberra has terrific leadership, both in entrepreneurship and also in Indigenous engagement, led by Tom Calma. The work that you do in engaging with Aboriginal and Torres Strait Islander communities is first rate. Notwithstanding the election result, Labor's passion for assisting the work that you do is as strong as ever. I look forward very much to hearing the contributions of the panelists today.
Authorised by Noah Carroll ALP Canberra.
speaking media what's new


text:
Jaipur-Ajmer-Pushkar-Fatehpur Sikri-Agra-Mathura - 3 D / 2 N
6,200 /- (Onwards per person)
Return : 3rd Day (22:00 Hrs.)
Family, Pilgrimage, Senior Citizen, Student
Rajasthan, Uttar Pradesh
Amber Fort, Birla Mandir, Jantar Mantar, Hawa Mahal, Albert Hall, City Palace, Jal Mahal, Taj Mahal, Agra Fort, Fatehpur Sikri, Brahma Temple At Pushkar, Dargah Ajmer, Mathura (Birth Place of Lord Krishna)
Rest of the Period you may book our Tour Code: NR-10 by Car/Innova/Tempo Traveller
By A.C. Volvo Coach with A.C. Room accommodation in a star hotel for 2 Nights at Jaipur.
1 06:00 Hrs Delhi - Jaipur 06:00 Hrs. Departure to Jaipur
12:00 Hrs. Arrival at Jaipur, Jaipur sight seeing upto
17.30 Hrs. Places Coverd : Birla Mandir, Albert Hall, Hawa Mahal, Jantar Mantar, City Palace, Jal Mahal, Amber Fort (Mirror Palace) Note: Those who are interested to see the famous theatre "Raj Mandir" can go on their own after completion of the sight seeing tour.
2 07:00 Hrs Jaipur - Ajmer - Pushkar - Jaipur 07:00 Hrs. Departure to Ajmer 131 Kms / 3 hrs, Places Coverd : Ajmer Dargah, then to Pushkar 11 kms. (here visit Brahma Temple) it is interesting to note that Pushkar is the only place in the world, where the temple of LordBrahma exists.
3 05:00 Hrs Jaipur - Fathepur Sikri - Agra - Mathura - Delhi 05:00 Hrs. Departure to Agra (240 kms / 5 hrs)
10:30 Hrs. Enroute visit Fatehpur Sikri Arrival at Agra. Sight seeing upto 16:00 Hrs., Places Covered: Taj Mahal, Agra Fort
16:00 Hrs. Departure to Mathura (56 kms / 1.5 hrs)
17:00 Hrs. Arrival at Mathura (See the Birth Place of Lord Krishna- Jail) and ISKON Temple
19:00 Hrs. Departure to Delhi (145 kms / 3.5 hrs)
22:00 Hrs. Arrival at Delhi
Delhi - Jaipur
06:00 Hrs. Departure to Jaipur
Jaipur - Ajmer - Pushkar - Jaipur
07:00 Hrs. Departure to Ajmer 131 Kms / 3 hrs, Places Coverd : Ajmer Dargah, then to Pushkar 11 kms. (here visit Brahma Temple) it is interesting to note that Pushkar is the only place in the world, where the temple of LordBrahma exists.
Jaipur - Fathepur Sikri - Agra - Mathura - Delhi
05:00 Hrs. Departure to Agra (240 kms / 5 hrs)
Apr-2022 To Mar-2023
Adult on Twin Sharing 7,130/- 7,475/-
Adult on Triple Sharing 6,900/- 7,245/-
Child(5-11)Without Bed 6,670/- 7,015/-
Single Adult In a Room 8,625/- 9,430/-
Tour Departure date 13-Apr-2023 (45 Vacant) 20-Apr-2023 (45 Vacant) 27-Apr-2023 (45 Vacant) 04-May-2023 (45 Vacant) 11-May-2023 (45 Vacant) 18-May-2023 (45 Vacant) 25-May-2023 (45 Vacant) 01-Jun-2023 (45 Vacant) 08-Jun-2023 (45 Vacant) 15-Jun-2023 (45 Vacant) 22-Jun-2023 (45 Vacant) 05-Oct-2023 (45 Vacant) 12-Oct-2023 (45 Vacant) 19-Oct-2023 (45 Vacant) 26-Oct-2023 (45 Vacant)
Jewellery, paintings, leatherwear, stone carving, textile, blue pottery, carpets, terracotta, wooden artefacts etc.
Also known as Amer Fort, Amber Fort is one of the principal tourist attractions in the Jaipur and is located high on a hill. Amer Fort was built by Raja Man Singh and is known for its artistic style, blending both Hindu and Rajput elements. The aesthetic ambiance of this incredible fort is seen within its walls on a four level layout plan. The palace served as a residence for the Rajput Maharajas and their families. The Amer town itself, which is an integral and inevitable entry point to the Amer Palace, is now a heritage town. A particular attraction at Amer Fort is the "magic flower" fresco carved in marble around the mirror palace which is identified by two hovering butterfly depiction. The flower has seven unique designs of a fish tail and each is viewed by a particular way of partial hiding of the panel with hands.
Birla Mandir
The Birla Temple, built by BD Birla is the major tourist attraction in the Jaipur city. This temple is also known as Laxmi Narayan Temple as it is dedicated to Lord Vishnu and his spouse Goddess Lakshmi. This temple is located on an elevated ground at the base of Moti Dungri hill. It is one of the major attractions of Jaipur because of its remarkable features. It looks stunning and mesmerizes the onlookers when it is brightly lit in the night. Three huge domes of the temple represent three different approaches to the religion. The stained glass windows of temple depict the scenes from Hindu mythology. It is surrounded by lush green gardens which complete its magnificent look.
Jantar Mantar
The Jantar Mantar is a collection of architectural astronomical instruments, built by Maharaja Jai Singh II between 1727 and 1734. Early restoration work on the same was undertaken under the supervision of Major Arthur Garrett, a keen amateur astronomer. The name is derived from Jantar, instrument, and Mantar, formula, therefore, Jantar Mantar means literally 'calculation instrument'. Maharaja constructed a total of five such facilities at different locations, including the ones at Delhi and Jaipur. The Jaipur observatory is the largest and best preserved. It has been declared a World Heritage Site by UNESCO.
Hawa Mahal
Hawa Mahal, also known as Palace of the Breeze was built in 1799 AD by Maharaja Sawai Pratap Singh and designed by Lal Chand Ustad in the form of the crown of Krishna. Its unique five-storied exterior is also akin to the honeycomb of the beehive with its 953 small windows called jharokhas. The original intention of the lattice was to allow royal ladies to observe everyday life in the street below without being seen. Built of red and pink sandstone, the palace is situated in the heart of Jaipur. It is a part of the City Palace and extends to the women's chambers. It particularly looks outstanding when viewed early in the morning, lit with the golden light of sunrise.
Albert Hall
Albert Hall Museum is the oldest museum in the state of Rajasthan. The building was designed by Sir Samuel Swinton Jacob and was opened as a public museum in 1887. It has a rich collection of paintings, carpets, ivory, stone, metal sculptures, colorful crystal works, etc. It is situated in the Ram Niwas Garden and is a fine example of Indo-Saracenic architecture. It is named after King Albert Edward VII. Maharaja Ram Singh initially wanted this building to be a town hall, but his successor decided it to be a museum for the art of Jaipur.
The City Palace was the seat of the Maharaja of Jaipur and it has the Chandra and Mubarak Mahal palaces and other buildings in its complex. The Chandra Mahal palace is now a museum but most of it is still a royal residence. The palace complex is located in the north-east of the grid patterned Jaipur city and incorporates an impressive array of courtyards, gardens and buildings. The palace was built between 1729 and 1732, by Sawai Jai Singh II, the ruler of Amber. The Maharani Palace, Baggi Khana are other important parts of the complex. The Govind Dev Ji temple is a part of the complex and its ceiling is ornamented in gold.
Jal Mahal, also known as Water Palace is located in the middle of the Man Sagar Lake in Jaipur city. The palace and the lake around it were renovated by Maharaja Jai Singh II of Amber. Recently, it has got an eye-popping makeover. Traditional boat-makers have crafted the Rajput style wooden boats and a gentle splashing of oars on the clear lake waters takes visitors to Jal Mahal. Visitors move past decorated chambers on the first floor to climb all the way up to the Chameli Bagh. Across the lake, Aravalli hills can be viewed dotted with temples and ancient forts, along with Jaipur, on the other side.
The Taj Mahal was built by Mughal emperor Shah Jahan in memory of his third wife, Mumtaz Mahal and is regarded by many, as the finest example of Mughal architecture. The Taj Mahal is a white marble mausoleum located in Agra, widely recognized as 'the Jewel of Muslim Art' in India and is one of the universally admired masterpieces of the world heritage. Taj Mahal has an architectural style that combines elements from Persian, Ottoman Turkish and Indian architectural styles. The Taj Mahal is surrounded by beautiful gardens. Its beauty attracts numerous Indian and international tourists to visit this site.
Fatehpur Sikri is a city and built near the much older Sikri. Akbar named the city, Fatehabad, with Fateh, a word of Arabic origin in Persian, meaning "victory"; it was later called Fatehpur Sikri. The city served few Mughal kings as their capital. According to historians, Akbar, the great Mughal emperor took great interest in the building of Fatehpur Sikri and also dictated its architectural style. Akbar planned the complex of building on Persian principles. The Easy availability of sandstone in the neighboring areas also meant that all the buildings here were made of the red stone. The imperial Palace complex of city consists of independent pavilions arranged in formal geometry on a piece of level ground.
Brahma Temple At Pushkar
The Brahma Temple is located at Pushkar which is about 11 km from Ajmer. The lake at Pushkar is believed to be created by Lord Brahma and has the same sanctity for Hindus, as Manasarovar in Tibet. It is interesting to note that Pushkar is the only place in northern India where the temple of Lord Brahma exists. The temple is believed to be 2000 years old while the present temple arrangement dates to the 14th century. The temple is mainly built of marble and stone stabs. The temple sanctum sanctorum holds the central images of Brahma and second consort Gayatri. A festival dedicated to Lord Brahma is held on the Kartik Purnima and the place is visited by a large number of pilgrims during this festival.
Dargah Ajmer
Ajmer has a historic importance as Mohammed Ghazni invaded the city many times from Afghanistan. Later, it became a favorite residence of the Mughals. It is an important place for Muslim Pilgrims. The Dargah is the tomb of Sufi Saint - Khwaja Moinuddin Chisti, who came to Ajmer from Persia in the year 1192. The Dargah was completed by Mughal Emperor Humayun. The main gate to the shrine is the Nizam Gate, followed by Shahjahani Gate, which was erected by emperor Shah Jahan. The annual Urs festival commemorates the death anniversary during the first six days of the Rajab. In honor of the saint, the Qawwali concerts are held reciting Chishti's own works during the Urs. A large number of devotees are attracted to the shrine during the festival.
Ajmer Sharif
Brahm Temple


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"A Twentieth Century Doctor of the Church"
January 26, 2009 by Pat McNamara
"A Twentieth Century Doctor of the Church" January 26, 2009 Pat McNamara
Today marks the death of Dietrich von Hildebrand (1889-1977), philosopher and academic. The son of a prominent sculptor, he grew up in Florence and returned to Germany to study philosophy. In 1912 he received his doctorate from the University of Göttingen. He converted to Catholicism in 1914, and during World War I he served in a military hospital. He later taught at the University of Munich. His opposition to National Socialism was well known, and he left Germany when Hitler came to power. In Austria he founded an anti-Nazi paper, but he fled to France after the German takeover in 1938. He then taught at the Catholic University of Toulouse. When the Germans occupied France he fled to America, where he joined the Fordham University faculty. In addition to his philosophical writings, Hildebrand also wrote theological works like Transformation in Christ (1948) and Christian Ethics (1953). In his later years, he was highly disenchanted with the postconciliar Church, but he remains one of the most important Catholic philosophers in the twentieth century. Pope Pius XII, who knew Hildebrand while he was papal nuncio in Germany, called him a "twentieth century Doctor of the Church." Pope Benedict XVI has expressed his belief that when "the intellectual history of the Catholic Church in the twentieth century is written, the name of Dietrich von Hildebrand will be most prominent among the figures of our time."
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Vermont health officials are warning people who live in Pittsford and the surrounding communities that they may be at increased risk for contracting eastern equine encephalitis, or EEE.
Mosquito born illnesses, like Eastern Equine Encephalitis and West Nile Virus are on the rise across the country. The deaths this month of two Vermonters from Eastern Equine Encephalitis have heightened concern about such illnesses here in Vermont.
The Vermont Health Department is planning to begin aerial spraying as part of a broader effort to control mosquitoes in an area of Rutland and Addison counties where two people were sickened, and one person died, from the state's first cases of Eastern Equine Encephalitis.
One of the two people in Vermont infected with eastern equine encephalitis has died.
Vermont's first two human cases of Eastern Equine Encephalitis have been identified in Rutland and Addison counties. And now state officials plan to spray pesticides from aircraft as a way to control potentially dangerous mosquitoes.


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Bose SoundSport Pulse review
Solid and sporty wireless earphones that deliver an impressive sound Tested at £170
Not quite perfect, but these are the best-sounding pair of wireless in-ears we've tested
Excellent wireless reliability
Fun bass
Decent HR sensor
More comfy than they look
Short battery life
Bose doesn't just make active noise cancellation earphones that zap the sound of outside noise.
The SoundSport Pulse wireless earphones have an inbuilt heart rate sensor to let you see how hard you're working during your runs or gym sessions.
At £170, they're not cheap, but the tech and sound are both solid.
Build and comfort
Comfort is perhaps the most common strong point among Bose headphones. The giant earpieces of the Bose SoundSport Pulse wireless look like they might buck the trend, but thankfully they don't.
The SoundSport Pulse wireless use soft silicone in-ear hooks, and these are the only parts that come into contact with your ears.
As the actual earphones are much lighter than they look, these are actually surprisingly comfortable earphones. Bose's reputation for great comfort is intact.
They're not exactly lookers though. The black earpieces stick out from your ears quite a way, and are far more conspicuous than previous Bose models.
MORE: Best headphone deals: in-ear, over-ear, wireless and more
You can hook them up to your phone using Bluetooth, but they also have NFC to let you pair devices just by touching the two together.
Wireless performance is excellent, with great stability and real-world range bang on the claimed nine metres as long as you don't put walls between the Bose SoundSport Pulse wireless and the source.
The downside of a tech-packed approach is that these headphones don't last that long from a charge.
Five hours of use won't cut it for all-day use, although the Bose SoundSport Pulse wireless are really best suited for runners, gym fans and those looking for a pair for their work commute.
They're recharged using a microUSB hidden under a flap on one earpiece.
MORE: Best wireless Bluetooth headphones
There's no active noise cancellation here and you can't use them wired, but there is a heart rate sensor built into the left earpiece. It's far more useful than the optical sensors used in smartwatches, whose accuracy tends to nosedive as soon as you start moving.
The Bose Connect app displays your current heart rate, but it's not desperately useful as it doesn't record changes in heartbeat throughout a workout. There's just a live read-out. However, the information can be sent to most of the top fitness apps, including Strava, Endomondo and MapMyRun, making it more meaningful.
At times the system failed to pick up on our heart rhythm, and it can take a handful of seconds for it to settle down to an accurate reading, but it's far less of a chore to use than an ANT+ chest strap.
The Bose SoundSport Pulse wirelesses also have a three-button remote, which is where the NFC chip lives, and there's a shirt clip on the neckband to stop the wire from banging against your neck.
The sound is enjoyable. It's rich and smooth, with powerful bass that's particularly handy if you're running out in a noisy environment, which can cut down the perceived bass level.
Perhaps more than anything else, this is a fun sound, one that's going to be easy to listen to for hours on end.
A focus on enjoyment rather than insight or ultra-precision detail won't please everyone, but it's a perfect fit for this style of earphone.
MORE: Best in-ear headphones 2016
There's some mid-bass padding that makes the Bose SoundSport Pulse wireless in-ears a little less clear and nimble-sounding than normal £170 earphones.
However there's invariably some compromise on sound when some of the budget has been spent on wireless tech rather than being piled into headphone basics.
Again, this fuller tone is perfect when the earphones are likely to need to compete with the noise of a gym or the city.
Alternatives may boast better battery life, but few sporty wireless sets will have a more consistent, cohesive sound.
There are improvements to be made in the Bose SoundSport Pulse wireless earphones. Future versions are likely to have better battery life, with any luck, and smaller earpieces.
But if the odd look and potential for every-day charging aren't off-putting, these are very solid sport earphones.
The sound is fun and consistent, and the comfort far better than you'd guess to look at this pair.
MORE: Best budget sports headphones
See all our Bose reviews


I've been really intrigued by the "Beauty Redefined" project that two LDS twin sisters have been organizing. Starting this month billboards are going to be going up all over Utah with positive messages about women and body image. (Oh, how I hope and pray that at least ONE of them is right next to the half dozen billboards on I-15 for breast enhancements and liposuction!) I am really inspired with what these girls are doing and hope that this movement and project catches on. If you are interested you can go here to read what some of their billboards are going to say. I especially like the one "When beauty hurts, we're doing it wrong"!
Their project has got me thinking a lot about beauty and what it truly means to be "beautiful." I remember when I was younger I was a bit discouraged by the fact that most of the important women in the scriptures are always described as being very physically attractive. For example, in his vision of Mary, the Mother of Christ Nephi describes her as "exceedingly fair" (1 Nephi 11:13), Rachel is described as being "beautiful and well favored" (Genesis 29:17), Esther is "fair and beautiful" (Esther 2:7) Abigail is of a "beautiful countenance" (1 Sam. 25:3) and Sarah is apparently so beautiful that even at 90-years-old she causes the King of the Philistines to fall in love with her (Genesis 20). In my teenage mind it seemed to me that only really beautiful girls were the ones "chosen" by God to do the important things in the scriptures. The plain ones, like Leah who is described as "tender eyed" ( which may have indicated she was crossed eyed or had another eye problem, Genesis 29:17), tended to take the back seat in the stories and had it sort of rough. I thought that being beautiful-- physically-- was a virtue in and of itself and that if you were beautiful then it somehow meant you were worth more to God.
Yet over the years as I've studied these women's lives more closely I've come to see that when the scriptures talk about "beauty" they aren't usually referring to physical attractiveness but rather a beauty that comes from being close to God. I think Sarah's story is a good illustration of this. In Genesis 20 we read about how Abraham and Sarah travel towards the land of the Philistines and how once again Abraham asks Sarah to say that she is his sister instead of his wife in order to protect his life. Yet, just like had happened before with the King of Egypt 40 or so years earlier, Abimelech the king of the Philistines sees Sarah and desires her. She is taken into the King's house and it is only through a remarkable dream that Abimelech is told that Sarah is Abraham's wife and therefore doesn't go in unto her. Now I've seen some very beautiful elderly women in my life but I still find it hard to imagine how Sarah, at 90-years- old, could be physically attractive enough that a King would whisk her away from her family. Granted, Sarah did live will into her 100's and so 90 was probably more "young" back then than it is now, but even she freely describes herself as an old woman.
"deep beauty"... It is the kind of beauty that cannot be painted on, surgically created, or purchased. It is the kind of beauty that doesn't wash off. It is spiritual attractiveness. Deep beauty springs from virtue. It is the beauty of being chaste and morally clean... When you are virtuous, chaste, and morally clean, your inner beauty glows in your eyes and in your face... We have been taught that "the gift of the Holy Ghost … quickens all the intellectual faculties, increases, enlarges, expands and purifies all the natural passions and affections. … It inspires virtue, kindness, goodness, tenderness, gentleness and charity. It develops beauty of person, form and features." Now, that is a great beauty secret! That is the beauty... that really matters and the only kind of beauty that lasts. "
Sarah had deep beauty. Mary had deep beauty, as did Rachel, Esther and Abigail. These women may have been beautiful physically by the standards of their time yet I think what made these women go down in the history books as "beautiful" was because they were close to God, they lived virtuous lives, and they knew who they were and what their missions were on earth. That is a type of beauty that can't be bought at the store or the doctor's office and therefore is precious above all else.
Yet you want to know the most wonderful part about "deep beauty"? You don't have to be rich to afford it, you don't have to have the right body size or hair color, you don't have to be free from disease or imperfections, and you don't have to have certain clothes or make-up. All it requires is drawing near to the heavenly parents who created you and becoming more like them... and that is something that is within every woman's reach.
Hmm... do you think that maybe I could fit all that on a billboard?
I was just thinking about this subject the other day myself. Here is a link to what I wrote.
Can't tell you how much I enjoy your posts. It always give me something to think about.
I totally love this today. It is beautiful.
LOVE. Thank you for this post!
Not to derail your post, but I think this perspective can also help us when we think about Book of Mormon language about cursedness vs. fairness.
Thank you SO MUCH for sharing this! I read a lot of things on their website that I hadn't really thought of before. I live basically right in Salt Lake County, and there is a billboard near our home with a picture of two small watermelons with the line "if life gives you lemons..." and then gives the contact info of a plastic surgeon.
For me this billboard is particularly annoying. I have successfully exclusively nursed two children with my "lemons" (probably more like pecans, but hey, they get the job done, which is what matters) I am very active, and I love to run, and I hear my "well-endowed" friends talk about how hard it is to run with large breasts and I wonder why anyone would ever want them if all my friends/family who have them don't particularly care for them. Thankfully my mother was similar size to me and never made a big deal about it. My sister is the same way, too, so we've just always gone through our lives being small and loving our bodies.
lovely! I sent this on to my teenage daughters. Thank you.
This is wonderful! Thank you for the Beauty Redefined shout-out and support. What a fantastic blog to be included in! Your concerns with all the "beauty" mentioned in scripture sound exactly like concerns I used to have, and you have hit the nail on the head as far as your beautiful, inspirational conclusions about what "beauty" signifies there. This is spiritual insight that every woman should consider. Thanks again for your support and kind words. The Beauty Redefined project is both a spiritual and academic mission for my sister and I, even though we don't make it explicitly religious due to our diverse audiences. You have placed the conversation beautifully within a religious perspective!
I'm so glad I just found you! What a great example and teacher you are. I'm so excited to catch up on your prior posts!
I may need to read this post every morning for the rest of my life for it to sink in.


Cans of Beans has MOVED! If you haven't already, please update your bookmarks to cansofbeans.com for new comic pages. For those who followed Cans of Beans through cansofbeans.thecomicseries.com, thanks for reading along!
Troubleshooting Notes: If you're still seeing the old site (this layout) when accessing cansofbeans.com, try clearing your cache. If that doesn't work, try accessing again tomorrow. It could mean that your DNS hasn't updated to the new IP address.
Okay, so what if I use ComicFury to access this webcomic?
You can still read through the first 3 chapters and most of the 4th on here, I'm not gonna be deleting them off the site. But if you want to read any new pages, it'll be on cansofbeans.com and not on thecomicseries.com/webcomic.ws or any of the ComicFury subdomains.
That's odd! What browser are you using?
Brosmith is an unusual name. How did you come up with it? Was it based on some one you knew/know?


First, make the bread! I like to triple or quadruple the batch. Stores well in the fridge in a baggie for several days.
preheat oven to 350 degrees. Spread batter onto parchment lined baking sheet into two rounds. Bake for 10 minutes.