Gravitational perfect fluid collapse in f(R) gravity

In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric f(R) gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude that the constant scalar curvature term f(R ₀) acts as a source of repulsive force and thus slows down the collapse of matter. The comparison with the corresponding results available in general relativity indicates that f(R ₀) plays the role of the cosmological constant.     

Modified gravity in a viscous and non-isotropic background

We study the dynamical evolution of an f(R) model of gravity in a viscous and anisotropic background which is given by a Bianchi type-I model of the Universe. We find viable forms of f(R) gravity in which one is exactly the Einsteinian model of gravity with a cosmological constant and other two are power law f(R) models. We show that these two power law models are stable with a suitable choice of parameters. We also examine three potentials which exhibit the potential effect of f(R) models in the context of scalar tensor theory. By solving different aspects of the model and finding the physical quantities in the Jordan frame, we show that the equation of state parameter satisfy the dominant energy condition. At last we show that the two power law f(R) models behave like quintessence model at late times and also the shear coefficient viscosity tends to zero at late times.     

Viability bounds in f(R,G) gravity with energy conditions

In the present work, we discuss the viability bounds arising from the energy conditions in the context of an extended gravitational theory namely f(R, G) gravity, where R stands for the curvature scalar and G represents the Gauss-Bonnet invariant. Two specific forms of f(R, G) have been taken into account to examine the validity of the general inequalities obtained by the weak energy condition (WEC). More specifically, we consider the constraints imposed by the weak energy condition (WEC) and verify whether the parameter range of the recent proposed models are consistent with the energy conditions.     

Newtonian and post Newtonian expansionfree fluid evolution in f(R) gravity

We consider a collapsing sphere and discuss its evolution under the vanishing expansion scalar in the framework of f(R) gravity. The fluid is assumed to be locally anisotropic which evolves adiabatically. To study the dynamics of the collapsing fluid, Newtonian and post Newtonian regimes are taken into account. The field equations are investigated for a well-known f(R) model of the form R+δR ² admitting Schwarzschild solution. The perturbation scheme is used on the dynamical equations to explore the instability conditions of expansionfree fluid evolution. We conclude that instability conditions depend upon pressure anisotropy, energy density and some constraints arising from this theory.     

Accelerated expansion from?a?modified-quadratic gravity

We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f(φ)R+f(R) where f(φ)=φ ² and f(R)=AR ²+BR _μν R ^μν,(A,B)∈ℝ. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w≈−0.2 and is accelerated in time with a scale factor evolving like a(t)∝t ^5/3 and B+3A≈0.036. When, B+3A→∞ which corresponds for the purely quadratic theory, the scale factor evolves like a(t)∝t ^1/2 whereas when B+3A→0 which corresponds for the purely scalar tensor theory we found when a(t)∝t ^1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=hH[(f)\dot]/f,h ? \mathbbRR=\eta H\dot{\phi}/\phi,\eta\in\mathbb{R} and H=g[(f)\dot]^c,(g,c) ? \mathbbRH=\gamma\dot{\phi}^{\chi},(\gamma,\chi)\in\mathbb{R}. It was shown that for some special values of  χ, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.     

The study of Gödel type solutions in f(R, ϕ) gravity

The aim of this paper is to study the Gödel type universe in modified f(R, ϕ) theory of gravity, where R stands for Ricci scalar and ϕ be the scalar potential. We investigate the modified field equations by using anisotropic and perfect fluid distributions. In particular, we consider two proposed models with some fixed values of parameters and investigate the exact solutions. The behaviour of energy conditions can be seen by a detailed graphical analysis. Furthermore, Tolman-Oppenheimer-Volkoff equation has been studied for both models in this theory. We have also discussed some exact solutions using perfect fluid. It is concluded that f(R, ϕ) theory of gravity support the phenomenon of cosmic expansion of the universe through Gödel type universe for both models.     

ΛCDM, ΛDGP and extended phantom-like cosmologies

In this paper we compare outcomes of some extended phantom-like cosmologies with each other and also with ΛCDM and ΛDGP. We focus on the variation of the luminosity distances, the age of the universe and the deceleration parameter versus the redshift in these scenarios. In a dynamical system approach, we show that the accelerating phase of the universe in the f(R)-DGP scenario is stable if one consider the curvature fluid as a phantom scalar field in the equivalent scalar-tensor theory, otherwise it is a transient and unstable phenomenon. Up to the parameters values adopted in this paper, the extended F(R,ϕ)-DGP scenario is closer to the ΛCDM scenario than other proposed models. All of these scenarios explain the late-time cosmic speed-up in their normal DGP branches, but the redshift at which transition to the accelerating phase occurs are different: while the ΛDGP model transits to the accelerating phase much earlier, the F(R,ϕ)-DGP model transits to this phase much later than other scenarios. Also, within the parameter spaces adopted in this paper, the age of the universe in the f(R)-DGP model is larger than ΛCDM, but this age in F(G,ϕ)-DGP is smaller than ΛCDM.     

Functional form of f(R) with power-law expansion in anisotropic model

In this paper, we study an anisotropic Bianchi-I space-time model in f(R) theory of gravity in the presence of perfect fluid as a matter contains. The aim of this paper is to find the functional form of f(R) from the field equations and hence the solution of various cosmological parameters. We assume that the deceleration parameter to be a constant, and the shear scalar proportional to the expansion scalar to obtain the power-law form of the scale factors. We find that the model describes the decelerated phases of the universe under the choice of certain constraints on the parameters. The model does not show the acceleration expansion and also transition from past deceleration to present accelerating epoch. We discuss the stability of the functional form of f(R) and find that it is completely stable for describing the decelerating phase of the universe.     

Noether gauge symmetry for f(R) gravity in Palatini formalism

In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Palatini f(R) theory of gravity. Using the dynamical equivalence between f(R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f(R) Lagrangian we find out the form of f(R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f(R) yield a power-law expansion for the scale factor of the universe.     

Existence of wormhole solutions and energy conditions in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

This paper is devoted to investigate the spherically symmetric wormhole models in f(R, T) gravity, where T and R are trace of stress energy tensor and the Ricci scalar, respectively. In this context, we discuss three distinct cases of fluid distributions viz, anisotropic, barotropic and isotropic matter contents. After considering the exponential f(R, T) model, the behavior of energy conditions are analyzed that will help us to explore the general conditions for wormhole geometries in this gravity. It is inferred that the usual matter in the throat could obey the energy conditions but the gravitational field emerging from higher order terms of modified gravity favor the existence of the non-standard geometries of wormholes. The stability as well as the existence of wormholes are also analyzed in this theory.     

Some Bianchi type cosmological models in f(R) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B ⁿ , where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.     

Anisotropic cosmological models in f(R,T) gravity according to holographic and new agegraphic dark energy

The paper deals with a spatially homogeneous and anisotropic universe filled with perfect fluid and dark energy components. We consider the f(R,T) theory according to holographic and new agegraphic dark energy in the Bianchi type I universe. In this study, we concentrate on two particular models of f(R,T) gravity namely, R+2f(T) and f(R)+λT. We conclude that the derived f(R,T) models can represent phantom or quintessence regimes of the universe.     

Noether gauge symmetry approach in f(R) gravity

We discuss the f(R) gravity model in which the origin of dark energy is identified as a modification of gravity. The Noether symmetry with gauge term is investigated for the f(R) cosmological model. By utilization of the Noether Gauge Symmetry (NGS) approach, we obtain two exact forms f(R) for which such symmetries exist. Further it is shown that these forms of f(R) are stable.     

Dynamics of some cosmological solutions in modified f(R) gravity

This paper is devoted to investigate the modified f(R) theory of gravity, where R represents the Ricci scalar respectively. For our current work, we consider the Friedmann-Robertson-Walker (FRW) space-time for finding solutions of field equations. Furthermore, some numerical solutions are examined by taking the Klein-Gordon Equation and using distinct values of the equation of state (EoS) parameter. In this way, we have discussed the solutions for acceleration expansion of the Universe, sub-relativistic Universe, radiation Universe, ultra-relativistic Universe, dust Universe, and stiff fluid Universe respectively. Moreover, their behaviours are examined by using power-law and exponential law techniques. The bouncing scenario is also discussed by choosing some particular values of the model parameters and observed the energy conditions, which are satisfied for a successful bouncing model. It is also concluded that some solution in f(R) theory of gravity supports the concept of exotic matter and accelerated expansion of the Universe due to a large amount of negative pressure.     

Scalar field instability in multi-dimensional cosmology

The scalar field theory on the background of cosmological models with n(n ≥ 1) spaces of constant curvature is considered. We take the integrable case of Ricci flat internal spaces. The coupling between the scalar and the gravitational fields includes the minimal coupling as well as the conformal case. In the ground state of the scalar field we find the conditions for vacuum instability realized for most of the possible solutions to Einstein's equations if the coupling parameter takes appropriate values. For the excited states of the scalar field we show the induction of massive modes and discuss their properties.     

Reconstruction of f(R,T) gravity in anisotropic cosmological models of accelerating universe

In this paper, we search the existence of Bianchi type I cosmological model in f(R,T) gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the trace of the stress-energy tensor T. We obtain the gravitational field equations in the metric formalism, and reconstruct the corresponding f(R,T) functions. Attention is attached to the special case, f(R,T)=f ₁(R)+f ₂(T) and two examples are assumed for this model. In the first example, we consider the unification of matter dominated and accelerated phases with f(R) gravity in anisotropic universe, and in the second instance, model of f(R,T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, f(R,T) is proportional to a power of R with exponents depending on the input parameters.     

Stability of a class of non-static axial self-gravitating systems in f(R) gravity

In this paper, we analyze stability regions of a non-static restricted class of axially symmetric spacetime with anisotropic matter distribution. We consider f(R)=R+?R ² model and assume hydrostatic equilibrium of the axial self-gravitating system at large past time. Considering perturbation from hydrostatic phase, we develop dynamical as well as collapse equations and explore dynamical instabilities at Newtonian and post-Newtonian regimes. It is concluded with the help of stiffness parameter, Γ ₁, that radial profile of physical parameters like pressure anisotropy, energy density and higher curvature terms of the f(R) model affect the instability ranges.