The plane symmetric vacuum solutions of modified field equations in metric f(R) gravity

The f(R) theories of gravity have been interested in recent years. A considerable amount of work has been devoted to the study of modified field equations with the assumption of constant Ricci scalar which may be zero or nonzero. In this paper, the exact vacuum solutions of plane symmetric spacetime are analyzed in f(R) theory of gravity. The modified field equations are studied not only for R=constant but also for general case R≠constant. In particular, we show that the Novotný-Horský and anti-de Sitter spacetimes are the exact solutions of the field equations with the non-zero constant Ricci scalar. Finally, the family of solutions with R≠constant is obtained explicitly which includes the Novotný-Horský, Kottler-Whittaker, Taub and conformally flat spacetimes.     

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.     

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.     

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.     

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.     

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.     

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.     

Collapsing stellar structures in f(R) gravity using Karmarkar condition

Our study illuminates the effects of gravitational collapse by considering heat flux anisotropic matter sources within the framework of the $f\left(R\right)$ theory of gravity. We assume the non-static spherically symmetric configuration to narrate the nature of the interior spacetime and match it with the Vaidya exterior geometry. Further, we employ the well-known Karmarkar condition, as it reduces the solution-generating method of field equations to a single metric potential. To ensure the viability of our collapsing system, a comprehensive graphical analysis is presented in the context of the Logarithmic-corrected $R^2$ gravity model. Our investigation argues that there are no traces of trapped surfaces in the collapsing procedure. Thus, naked singularity and black hole are not the final fate of the gravitational collapse.     

New holographic dark energy in modified f(R) Horava-Lifshitz gravity

In this paper, we study the new holographic dark energy model in the framework of modified f(R) Horava-Lifshitz Gravity. We apply correspondence scheme to construct model the in underlying scenario using power-law form of scale factor. To explore accelerated expansion of the universe, some well-known cosmological parameters (equation of state parameter and squared speed of sound) and cosmological planes (ω _Λ – \(\omega'_{\varLambda}\) and statefinder) are discussed for reconstructed model. It is interesting to conclude that these parameters represent phantom behavior of the universe with stable configuration. also, the cosmological planes show compatible results with recent observations for accelerated expansion of the universe.     

Thin-shell wormholes in non-linear f(R) gravity with variable scalar curvature

The present paper explores a thin-shell wormhole (TSW) developed by employing the cut and paste method to two copies of the black hole. It develops TSW in modified $f\left(R\right)$ theory of gravity with variable scalar curvature. The effects of the model parameters on the wormhole solutions are tested, the regions of linear stability are analyzed and stable wormhole solutions have been obtained.     

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.