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F. Shojai

Publications and source records attributed to F. Shojai.

33 records · Page 2Linked to original sources
arXiv2018

On the classification of consistent boundary conditions for $ \mathit{f}(\mathit{R})$-Gravity

Using a completely covariant approach, we discuss the role of boundary conditions (BCs) and the corresponding Gibbons--Hawking--York (GHY) terms in $ \mathit{f}(\mathit{R}) $-gravity in arbitrary dimensions. We show that $ f(\mathit{R}) $-gravity, as a higher derivative theory, is not described by a degenerate Lagrangian, in its original form. Hence, without introducing additional variables, one can not obtain consistent BCs, even by adding the GHY terms (except for $f(\mathit{R})=R$). However, following the Ostrogradsky approach, we can introduce a scalar field in the framework of Brans-Dicke formalism to the system to have consistent BCs by considering appropriate GHY terms. In addition to the Dirichlet BC, the GHY terms for both Neumann and two types of mixed BCs are derived. We show the remarkable result that the $f(\mathit{R})$-gravity is itself compatible with one type of mixed BCs, in $D$ dimension, i.e. it doesn't require any GHY term. For each BC, we rewrite the GHY term in terms of Arnowit-Deser-Misner (ADM) variables.

gr-qc↗
arXiv2018

The Effect of $α$-Vacua on the Scalar and Tensor Spectral Indices: Slow-Roll Approximation

Since the duration of inflation is finite, imposing the initial condition in infinite past, i.e. the Bunch-Davies vacuum, is inherently ambiguous. In this paper, we resort to the mixed states as initial condition which are called the $α$-vacua and then introduce a physical momentum cutoff $Λ$ [Danielsson:2002kx], in which the evolution of perturbations begins. We show that the initial time $t_i$, when the initial condition is imposed, depends on the wave number of fluctuation, as it is for the time of horizon crossing, $t_q$. Then we calculate the corrections to the scalar and tensor power spectra and their corresponding spectral indices. Throughout this work, the calculation is done up to the first order in slow-roll parameters. We indicate that the leading order corrections to the spectral indices have a $q$-dependent amplitude, $2ε_{f}[2ε_{f}(\frac{q}{q_{f}})^{4ε+4η}-η_{f}(\frac{q}{q_{f}})^{3ε+ξ}]$ times a $q$-dependent oscillatory part, $\cos(\frac{2Λ(q/q_{f})^ε}{H_{f}})$, where $H$, $ε$, $η$, and $ξ$ are the Hubble and slow-roll parameters respectively, and the subscript $f$ denotes that these quantities are evaluated at the time when the first scale, $q_{f}$, satisfies the initial condition, i.e. $q=a(t_i)Λ$.

gr-qc↗
arXiv2018

On the initial conditions of scalar and tensor fluctuations in $f(R,ϕ)$ gravity

We have considered the perturbation equations governing the growth of fluctuations in generalized scalar tensor theory during inflation. we have found that the scalar metric perturbations at very early times are negligible compared with the scalar field perturbation, just like general relativity. At sufficiently early times, when $q/a\gg H$, we have obtained the metric and scalar field perturbation in the form of WKB solutions up to an undetermined coefficient. Then we have quantized the scalar fluctuations and expanded the metric and the scalar field perturbations with the help of annihilation and creation operators of the scalar field perturbation. The standard commutation relations of annihilation and creation operators fix the unknown coefficient. Going over to the gauge invariant quantities which are conserved beyond the horizon, we have obtained the initial condition of the generalized Mukhanov-Sasaki equation. And a similar procedure is performed for the case of tensor metric perturbation.

gr-qc↗
arXiv2016

On the Relativistic anisotropic configurations

In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov (TOV) equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behaviour of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.

gr-qc↗
arXiv2015

The equivalence principle and the relative velocity of local inertial frames

In this paper we explicitly show that in general relativity, the relative velocity of two local inertial frames is always less than the velocity of light. This fact is a by-product of the equivalence principle. The general result is then illustrated within two examples, the FLRW cosmological model and the Schwarzschild metric.

gr-qc↗
arXiv2015

On the Newtonian Anisotropic Configurations

In this paper we are concerned with the effects of anisotropic pressure on the boundary conditions of anisotropic Lane-Emden equation and homology theorem. Some new exact solutions of this equation are derived. Then some of the theorems governing the Newtonian perfect fluid star are extended taking the anisotropic pressure into account.

gr-qc↗
arXiv2014

An f(R) model for dark matter: rotation curves and gravitational lensing

There should be two ways to describe the flat rotation curves of galaxies and cluster of galaxies. Either one can introduce a dark matter component for the matter filling the halo, or by modifying the gravity theory and give the flat rotation curve a geometrical nature. Here we adopt an f(R) model suitable for describing the effect. After matching the solution with the exterior solution, the effective density, radial and tangential pressures are obtained. Then the energy conditions and lensing effect is investigated.

gr-qc↗
arXiv2013

Notes on the compatibility of type Ia supernovae data and varying--$G$ cosmology

Observational data for type Ia supernovae, shows that the expansion of the universe is accelerated. This accelerated expansion can be described by a cosmological constant or by dark energy models like quintessence. An interesting question may be raised here. Is it possible to describe the accelerated expansion of universe using varying--$G$ cosmological models? Here we shall show that the price for having accelerated expansion in slow--varying--$G$ models (in which the dynamical terms of $G$ are ignored) is to have highly non--conserved matter and also that it is in contradiction with other data.

gr-qc↗
arXiv2013

Tracker coupled quintessence

In this paper two tracker solutions for conformally coupled quintessence model is obtained. The first solution is determined by dividing the evolution of the universe to matter and dark energy dominated epochs and then the allowed bound on the equation of state parameter is obtained, such that a tracker behaviour is resulted. For the other solution, the quintessence potential is assumed to be a linear combination of two exponential functions. Then we have found an exact solution which can be tracker by adjusting some parameters.

gr-qc↗
arXiv2009

Statefinder diagnosis of nearly flat and thawing non-minimal quintessence

Non-minimally coupled scalar field models of dark energy are equivalent to an interacting quintessence in the Einstein's frame. Considering two special important choices of the potential of the scalar field, i.e. nearly flat and thawing potential, one has an analytical expression for the equation of state parameter as a function of the density parameter of the scalar field for any choice. Here we investigate the non-minimal quintessence model by applying the method of statefinder diagnosis to it and plotting the evolutionary trajectories of the statefinder parameters.

gr-qc↗
arXiv2007

Quantum cosmology with varying speed of light and Bohmian trajectories

The classical trajectories for FLRW universe with varying speed of light are obtained for the cases in which the cosmological constant depends or not depend on the velocity of light. The theory is then quantized and the corresponding WDW equation is solved. It is shown that the method of causal interpretation of Bohm can be applied successfully to the theory. Finally the Bohmian trajectories are obtained and compared with the classical ones.

gr-qc↗
arXiv2005

Classical and Quantum Limits in Bohmian Quantum Cosmology

In this paper we have investigated the classical limit in Bohmian quantum cosmology. It is observed that in the quantum regime where the quantum potential is greater than the classical one, one has an expansion in terms of negative powers of the Planck constant. But in the classical limit there are regions having positive powers of the Planck constant, and regions having negative powers and also regions having both. The conclusion is that the Bohmian classical limit cannot be obtained by letting the Planck constant goes to zero.

gr-qc↗