Search

The present work is devoted to explore some interesting cosmological features of a newly proposed theory of gravity namely $\mathcal{F}(R,L_m,T)$ theory, where $R$ and $T$ represent the Ricci scalar and trace of energy momentum-tensor, respectively. Firstly, a non-equilibrium thermodynamical description is considered on the apparent horizon of the Friedmann's cosmos. The Friedmann equations are demonstrated to be equivalent to the first law of thermodynamics, i.e., ${T_{Ah}d\varepsilon_{h}^\prime+T_{Ah}d_{i}\varepsilon_{h}^\prime=-d\hat{E}+\hat{W}dV}$, where ${d_{i}\varepsilon_{h}^\prime}$ refers to entropy production term. We also formulate the constraint for validity of generalized second law of thermodynamics and check it for some simple well-known forms of generic function $\mathcal{F}(R,L_m,T)$. Next, we develop the energy bounds for this framework and constraint the free variables by finding the validity regions for NEC and WEC. Further, we reconstruct some interesting cosmological solutions namely power law, $\Lambda$CDM and de Sitter models in this theory. The reconstructed solutions are then examined by checking the validity of GSLT and energy bounds. Lastly, we analyze the stability of all reconstructed solutions by introducing suitable perturbations in the field equations. It is concluded that obtained solutions are stable and cosmologically viable., Comment: 24 pages, 13 figures

The primary objective of this article is to study the energy condition bounds for spherical and hyperbolic wormholes in well-known $f(R,T)$ theory of gravity. For this purpose, we formulate the field equations for spherically and pseudospherically geometries using anisotropic matter and linear form of generic function $f(R,T)$. By imposing different conditions on radial and tangential pressures or by adopting some known choices for red shift and shape functions, we present the graphical analysis of energy conditions for both spherically and pseudospherically symmetric wormholes. It is seen that energy density for spherically symmetric wormhole is always positive for $\lambda>-4\pi$ and $\lambda<-8\pi$, while the energy conditions for radial pressure are negative at throat. Likewise, in case of pseudospherically symmetric wormhole, it is observed that energy density is always positive for negative $\lambda$, however conditions based on radial pressure may be positive or negative for the considered different cases., Comment: 20 pages, 15 figures, 01 table

The present article investigates the possibility of reconstruction of the generic function in $F(\mathcal{R},T)$ gravitational theory by considering some well-known cosmological bouncing models namely exponential evaluation, oscillatory, power law and matter bounce model, where $\mathcal{R}$ and $T$ are Ricci scalar and trace of energy-momentum tensor, respectively. Due to the complexity of dynamical field equations, we propose some ansatz forms of function $F(\mathcal{R},T)$ in perspective models and examine that which type of Lagrangian is capable to reproduce bouncing solution via analytical expression. It is seen that for some cases of exponential, oscillatory and matter bounce models, it is possible to get analytical solution while in other cases, it is not possible to achieve exact solutions so only complementary solutions can be discussed. However, for power law model, all forms of generic function can be reconstructed analytically. Further, we analyze the energy conditions and stability of these reconstructed cosmological bouncing models which have analytical forms. It is found that these models are stable for linear forms of Lagrangian only but the reconstructed solutions for power law are unstable for some non-linear forms of Lagrangian., Comment: 26 pages, 11 figures

In this manuscript, we explore the existence of wormhole solutions exhibiting spherical symmetry in a modified gravity namely $f(R,T)$ theory by involving some aspects of non-commutative geometry. For this purpose, we consider the anisotropic matter contents along with the well-known Gaussian and Lorentizian distributions of string theory. For the sake of simplicity in analytic discussions, we take a specific form of $f(R,T)$ function given by $f(R,T)=R+\lambda T$. For both these non-commutative distributions, we get exact solutions in terms of exponential and hypergeometric functions. By taking some suitable choice of free parameters, we investigate different interesting aspects of these wormhole solutions graphically. We also explored the stability of these wormhole models using equilibrium condition. It can be concluded that the obtained solutions are stable and physically viable satisfying the wormhole existence criteria. Lastly, we discuss the constraints for positivity of the active gravitational mass for both these distributions., Comment: 12 pages, 8 figures

The present study is elaborated to investigate the validity of thermodynamical laws in a modified teleparallel gravity based on higher-order derivatives terms of torsion scalar. For this purpose, we consider spatially flat FRW model filled with perfect fluid matter contents. Firstly, we explore the possibility of existence of equilibrium as well as non-equilibrium picture of thermodynamics in this extended version of teleprallel gravity. Here, we present the first law and the generalized second law of thermodynamics (GSLT) using Hubble horizon. It is found that non-equilibrium description of thermodynamics exists in this theory with the presence of an extra term called as entropy production term. We also establish GSLT using the logarithmic corrected entropy. Further, by taking the equilibrium picture, we discuss validity of GSLT at Hubble horizon for two $F$ different models. Using Gibbs law and the assumption that temperature of matter within Hubble horizon is similar to itself, we use different cases for choices scale factors to discuss the GSLT validity graphically in all scenarios. It is found that the GSLT is satisfied for a specified range of free parameters in all cases., Comment: 23 pages, 15 figures

We investigate the cosmological evolution in a new modified teleparallel theory, called $f(T,B)$ gravity, which is formulated by connecting both $f(T)$ and $f(R)$ theories with a boundary term $B$. Here, $T$ is the torsion scalar in teleparallel gravity and $R$ is the scalar curvature. For this purpose, we assume flat Friedmann-Robertson-Walker (FRW) geometry filled with perfect fluid matter contents. We study two cases in this gravity: One is for a general function of $f(T,B)$, and the other is for a particular form of it given by the term of $-T+F(B)$. We also formulate the general energy constraints for these cases. Furthermore, we explore the validity of the bounds on the energy conditions by specifying different forms of$f(T,B)$ and $F(B)$ function obtained by the reconstruction scheme for de Sitter, power-law, the $\Lambda$CDM and Phantom cosmological models. Moreover, the possible constraints on the free model parameters are examined with the help of region graphs. In addition, we explore the evolution of the effective equation of state (EoS) $\omega_{eff}$ for the universe and compare theoretical results with the observational data. It is found that the effective EoS represents the phantom phase or the quintessence one in the accelerating universe in all of the cases consistent with the observational data., Comment: 20 pages, 8 figures

In this paper, we discuss spherically symmetric wormhole solutions in $f(R,T)$ modified theory of gravity by introducing well-known non-commutative geometry in terms of Gaussian and Lorentizian distributions of string theory. For some analytic discussion, we consider an interesting model of $f(R,T)$ gravity defined by $f(R,T)=f_{1}(R)+\lambda T$. By taking two different choices for the function $f_{1}(R)$, that is, $f_{1}(R)=R$ and $f_{1}(R)=R+\alpha R^{2}+\gamma R^{n}$, we discuss the possible existence of wormhole solutions. In the presence of non-commutative Gaussian and Lorentizian distributions, we get exact and numerical solutions for both these models. By taking appropriate values of the free parameters, we discuss different properties of these wormhole models analytically and graphically. Further, using equilibrium condition, it is found that these solutions are stable. Also, we discuss the phenomenon of gravitational lensing for the exact wormhole model and it is found that the deflection angle diverges at wormhole throat., Comment: 15 pages, 18 figures

In this paper, we explore the nature of scalar field potential in $f(R, R_{\alpha\beta} R^{\alpha\beta},\phi)$ gravity using a well-motivated reconstruction scheme for flat FRW geometry. The beauty of this scheme lies in the assumption that the Hubble parameter can be expressed in terms of scalar field and vice versa. Firstly, we develop field equations in this gravity and present some general explicit forms of scalar field potential via this technique. In the first case, we take De Sitter universe model and construct some field potentials by taking different cases for coupling function. In the second case, we derive some field potentials using power law model in the presence of different matter sources like barotropic fluid, cosmological constant and Chaplygin gas for some coupling functions. From graphical analysis, it is concluded that using some specific values of the involved parameters, the reconstructed scalar field potentials are cosmologically viable in both cases., Comment: 30 pages, 3 figures

In this work, we explore wormhole solutions in $f(R,T)$ theory of gravity, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic, isotropic and barotropic fluids in three separate cases. By taking into account Starobinsky $f(R)$ model , we analyze the behavior of energy conditions for these different kind of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of spacetime. We also give the graphical illustration of obtained results and discuss the equilibrium picture for anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this gravity., Comment: 26 pages, 12 figures

The present paper is elaborated to discuss the energy condition bounds in a modified teleparallel gravity namely $F(T,T_{G})$, involving torsion invariant $T$ and contribution from a term $T_G$, the teleparallel equivalent of the Gauss-Bonnet term. For this purpose, we consider flat FRW universe with matter contents as perfect fluid. We formulate the SEC, NEC, WEC and DEC in terms of some cosmic parameters including Hubble, deceleration, jerk and snap parameters. By taking two interesting models for $F(T,T_{G})$ and some recent limits of these cosmic parameters, we explore the constraints on the free parameters present in both assumed models. We also discuss these constraints graphically in terms of cosmic time by taking power law cosmology into account., Comment: 24 pages, 11 figures

The present paper examines the validity of energy bounds in a modified theory of gravity involving non-minimal coupling of torsion scalar and perfect fluid matter. In this respect, we formulate the general inequalities of energy conditions by assuming the flat FRW universe. For the application of these bounds, we particularly focus on two specific models that are recently proposed in literature and also choose the power law cosmology. We find the feasible constraints on the involved free parameters and evaluate their possible ranges graphically for the consistency of these energy bounds., Comment: 20 pages, 10 figures, to appear in Astrophys. Space Sci

We explore Noether gauge symmetries of FRW and Bianchi I universe models for perfect fluid in scalar-tensor gravity with extra term $R^{-1}$ as curvature correction. Noether symmetry approach can be used to fix the form of coupling function $\omega(\phi)$ and the field potential $V(\phi)$. It is shown that for both models, the Noether symmetries, the gauge function as well as the conserved quantity, i.e., the integral of motion exist for the respective point like Lagrangians. We determine the form of coupling function as well as the field potential in each case. Finally, we investigate solutions through scaling or dilatational symmetries for Bianchi I universe model without curvature correction and discuss its cosmological implications.

The study of energy conditions has many significant applications in general relativistic and cosmological contexts. This paper explores the energy conditions in the framework of the most general scalar-tensor theory with field equations involving second-order derivatives. For this purpose, we use flat FRW universe model with perfect fluid matter contents. By taking power law ansatz for scalar field, we discuss the strong, weak, null and dominant energy conditions in terms of deceleration, jerk and snap parameters. Some particular cases of this theory like k-essence model and modified gravity theories etc. are analyzed with the help of the derived energy conditions and the possible constraints on the free parameters of the presented models are determined., Comment: 28 pages, 5 figures

The present study investigates the nature of the field potential via new technique known as reconstruction method for the scalar field potentials. The key point of this technique is the assumption that Hubble parameter is dependent on the scalar field. We consider Bianchi type I universe in the gravitational framework of scalar-tensor gravity and explore the general form of the scalar field potential. In particular, this field potential is investigated for the matter contents like barotropic fluid, the cosmological constant and Chaplygin gas. It is concluded that for a given value of Hubble parameter, one can reconstruct the scalar potentials which can generate the cosmology motivated by these matter contents., Comment: 20 pages, 4 figures. Phys. Lett. B (2013)

This paper is devoted to study the accelerated expansion of the universe by exploring the Brans-Dicke parameter in different eras. For this purpose, we take FRW universe model with viscous fluid (without potential) and Bianchi type I universe model with barotropic fluid (with and without potential). We evaluate deceleration parameter as well as Brans-Dicke parameter to explore cosmic acceleration. It is concluded that accelerated expansion of the universe can also be achieved for higher values of the Brans-Dicke parameter in some cases., Comment: 29 pages, 13 figures

In this paper, we investigate the nature of self-interacting potential that can support the accelerated expansion of the universe as indicated by observational data. For this purpose, we consider the Bianchi type I (BI) universe model in the Brans-Dicke (BD) field scenario and use a power law for both the scalar field and the scale factor. It is found that the accelerated expansion of the universe can be discussed for a positive power law potential with negative values of the BD parameter. We also explore the evolution of energy density perturbations. This analysis indicates that the model allows growing modes for negative values of the BD parameter and $m>0$., Comment: 23 pages, 6 figures

We explore locally rotationally symmetric Bianchi I universe in Brans-Dicke gravity with self-interacting potential by using charged viscous cosmological string fluid. We use a relationship between the shear and expansion scalars and also take the power law for scalar field as well as self-interacting potential. It is found that the resulting universe model maintains its anisotropic nature at all times due to the proportionality relationship between expansion and shear scalars. The physical implications of this model are discussed by using different parameters and their graphs. We conclude that this model corresponds to an accelerated expanding universe for particular values of the parameters., Comment: 17 pages, 6 figures

This paper is devoted to study Bianchi type I cosmological model in Brans-Dicke theory with self-interacting potential by using perfect, anisotropic and magnetized anisotropic fluids. We assume that the expansion scalar is proportional to the shear scalar and also take power law ansatz for scalar field. The physical behavior of the resulting models are discussed through different parameters. We conclude that in contrary to the universe model, the anisotropic fluid approaches to isotropy at later times in all cases which is consistent with observational data., Comment: 25 pages, 20 figures

This paper is devoted to study the energy content of colliding plane waves using approximate Noether symmetries. For this purpose, we use approximate Lie symmetry method of Lagrangian for differential equations. We formulate the first-order perturbed Lagrangian for colliding plane electromagnetic and gravitational waves. It is shown that in both cases, there does not exist, Comment: 18 pages, accepted for publication in Brazilian J Physics

In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to evaluate the third-order approximate symmetries of the orbital and geodesic equations. It is shown that energy must be re-scaled by some factor in the third-order approximation. We discuss the insights of this re-scaling factor., Comment: 14 pages, no figure, accepted for publication in Physica Scripta

This paper is devoted to study the energy problem in general relativity using approximate Lie symmetry methods for differential equations. We evaluate second-order approximate symmetries of the geodesic equations for the stringy charged black hole solutions. It is concluded that energy must be re-scaled by some factor in the second-order approximation., Comment: 18 pages, accepted for publication in Canadian J. Physics