Static wormhole solutions in f(R) gravity

In this work, we study static spherically symmetric wormhole solutions in f(R) gravity. We explore wormhole solutions for anisotropic and isotropic fluids as well as barotropic equation of state with radial pressure. The behavior of weak and null energy conditions is investigated in each case. It is found that these energy conditions are violated for both the anisotropic and isotropic case but are satisfied for barotropic fluids in particular regions. This confirms the existence of wormholes obeying the energy conditions in these regions.     

Neutron stars in generalized f(R) gravity

A gravity theory is considered with the Einstein-Hilbert Lagrangean R+aR ²+bR _μν R ^μν , R _μν being Ricci’s tensor and R the curvature scalar. The parameters a and b are taken of order 1 km². Arguments are given which suggest that the effective theory so obtained might be a fair approximation of a viable theory. A numerical integration is performed of the field equations for a free neutron gas. The result is that the star mass increases with increasing central density until about 1 solar mass and then decreases. The baryon number increases monotonically, which suggests that the theory allows stars in equilibrium with arbitrary baryon number, no matter how large.     

Cylindrical thin-shell wormholes in f(R) gravity

In this paper, we employ cut and paste scheme to construct thin-shell wormhole of a charged black string with f(R) terms. We consider f(R) model as an exotic matter source at wormhole throat. The stability of the respective solutions are analyzed under radial perturbations in the context of R+δR ² model. It is concluded that both stable as well as unstable solutions do exist for different values of δ. In the limit δ→0, all our results reduce to general relativity.     

Acceleration of the universe in f(R) gravity models

A general formalism for the investigation of the late time dynamics of the universe for any analytic f(R) gravity model, along with a cold dark matter, has been discussed in the present work. The formalism is then elucidated with two examples. The values of the parameters of the models are chosen in such a way that they are consistent with the basic observational requirement.     

Lookback time as a test for f(R) gravity in the Palatini approach

We use the recently released data of lookback time (LT)-redshift relation, the cosmic microwave background shift parameter and the baryon acoustic oscillation measurements to constrain cosmological parameters of f (R) gravity in the Palatini formalism by considering the f (R) form of type (a) f (R) = R β/Rn and (b) f (R) = R + α ln R β. Under the assumption of a Friedmann-Robertson-Walker universe, we achieved the best fitting results of the free parameters (Ωm0, n) for (a) and (Ωm0, α) for (b). We find tha...     

Generalized second law of thermodynamics in QCD ghost f(G) gravity

Considering power-law for of scale factor in a flat FRW universe we reported a reconstruction scheme for f(G) gravity based on QCD ghost dark energy. We reconstructed the effective equation of state parameter and observed “quintessence” behavior of the equation of state parameter. Furthermore, considering dynamical apparent horizon as the enveloping horizon of the universe we have observed that the generalized second law of thermodynamics is valid for this reconstructed f(G) gravity.     

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.     

A new class of Bianchi cosmological models in f(R,T) gravity

The new class of cosmological model of the early Universe is considered with f(R,T) modified theories of gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). The exact solutions to the corresponding field equations are obtained in quadrature form. The cosmological parameters have been discussed in detail. We have also discussed the well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance (d _L ) and distance modulus μ(z) with redshift.     

Inflation in mimetic f(R,T) gravity

In this paper, we employ mimetic $f(R,T)$ gravity coupled with Lagrange multiplier and mimetic potential to yield viable inflationary cosmological solutions consistent with latest Planck and BICEP2/Keck Array data. We present here three viable inflationary solutions of the Hubble parameter ($H$) represented by $H\left(N\right)={(A\exp \beta N+B{\alpha }^N)}^{\gamma }$, $H\left(N\right)={(A{\alpha }^N+B\log N)}^{\gamma }$, and $H\left(N\right)={(A{e}^{\beta N}+B\log N)}^{\gamma }$, where $A$, $\beta$, $B$, $\alpha$, $\gamma$ are free parameters, and $N$ represents the number of e-foldings. We carry out the analysis with the simplest minimal $f(R,T)$ function of the form $f(R,T)=R+\chi T$, where $\chi$ is the model parameter. We report that for the chosen $f(R,T)$ gravity model, viable cosmologies are obtained compatible with observations by conveniently setting the Lagrange multiplier and the mimetic potential.     

The generalized second law of thermodynamics for the interacting in f(T) gravity

We study the validity of the generalized second law (GSL) of gravitational thermodynamics in a non-flat FRW universe containing the interacting in f(T) gravity. We consider that the boundary of the universe to be confined by the dynamical apparent horizon in FRW universe. In general, we discuss the effective equation of state, deceleration parameter and GLS in this framewok. Also, we find that the interacting-term Q modifies these quantities and in particular, the evolution of the total entropy, results in an increases on the GLS of thermodynamic, by a factor $4\pi R_{A}^{3} Q/3$ . By using a viable f(T) gravity with an exponential dependence on the torsion, we develop a model where the interaction term is related to the total energy density of matter. Here, we find that a crossing of phantom divide line is possible for the interacting-f(T) model.     

Nonlinear electrodynamics in f(T) gravity and generalized second law of thermodynamics

In this paper, we study the nonlinear electrodynamics in the framework of f(T) gravity for FRW universe along with dust matter, magnetic and torsion contributions. We evaluate the equation of state and deceleration parameters to explore the accelerated expansion of the universe. The validity of generalized second law of thermodynamics for Hubble and event horizons is also investigated in this scenario. For this purpose, we assume polelike and power-law forms of scale factor and construct f(T) models. The graphical behavior of the cosmological parameters versus smaller values of redshift z represent the accelerated expansion of the universe. It turns out that the generalized second law of thermodynamics holds for all values of z with Hubble and event horizons in polelike scale factor whereas for power-law form, it holds in a specific range of z for both horizons.     

Generalized second law of thermodynamics in f(T) gravity with entropy corrections

We study the generalized second law (GSL) of thermodynamics in f(T) cosmology, where T is the torsion scalar in teleparallelism. We consider the universe as a closed bounded system filled with n component fluids in the thermal equilibrium with the cosmological boundary. We use two different cosmic horizons: the future event horizon and the apparent horizon. We show the conditions under which the GSL will be valid in specific scenarios of the quintessence and the phantom energy dominated eras. Further we associate two different entropies with the cosmological horizons: with a logarithmic correction term and a power-law correction term. We also find the conditions for the GSL to be satisfied or violated by imposing constraints on model parameters.     

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.