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 a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f (R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity.

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.

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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 off (T, B) and F (B) function obtained by the reconstruction scheme for de Sitter, power-law, the ΛCDM 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) ω ef f 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.

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.