Some Cosmological Aspects of Celestial Objects in Modified Gravity

Abstract

This thesis is devoted to analyze the existence as well as the dynamics of some celestial objects in various well-known modified gravity theories. In this framework, we explore the evolution of spherical self-gravitating structures in the realm of f(R), f(R, T) and f(G, T) theories, where R, T and G are the Ricci scalar, trace of stress energy tensor and the Gauss-Bonnet term, respectively. It has been a fascinating challenge to find the realistic configurations of stellar models in different modified theories gravity. In order to achieve this goal, we have considered the observational values of three notable strange compact stars, namely Her X-1, SAX J1808.4-3658, and 4U 1820- 30. The solutions obtained by Krori and Barua are used to examine the nature of particular compact stars with three different modified gravity models. The behavior of material variables is analyzed through plots. We also discuss the behavior of different forces, equation of state parameter, measure of anisotropy and Tolmann- Oppenheimer-Volkoff equation in the modeling of stellar structures. The comparison from our graphical representations may provide evidences for the realistic and viable f(R), f(R, T) and f(G, T) gravity models at both theoretical and astrophysical scale. We also investigate the wormhole solutions with spherically symmetric geometry in f(R, T) gravity. We discuss three different cases for matter contents namely, anisotropic, barotropic and isotropic fluid configurations. We consider few notable mathematical formulations of f(R, T) model to analyze the behavior of energy conditions and to explore the general conditions for wormholes in the framework of modified theories. It is observed that the usual matter in the throat may satisfy the energy conditions but the gravitational field emerging from higher order terms of modified xvi xvii gravity favor the existence of the non-standard geometries of wormholes. We represent this investigation via plots and examined the equilibrium picture in the background of anisotropic fluid. The stability and existence of these wormholes is also analyzed in this theory. Finally, the role of modified versions of structure scalars are analyzed in the modeling of relativistic spheres in f(R, T) gravity. We assume that non-static diagonally symmetric geometry is coupled with dissipative anisotropic viscous fluid distributions in the presence of f(R, T) dark source terms. A specific distributions of f(R, T) cosmic model has been assumed and the spherical mass function through generic formula introduced by Misner-Sharp has been formulated. Some very important relations regarding Weyl scalar, matter variables and mass functions are being computed. After decomposing orthogonally the Riemann tensor, some scalar variables in the presence of f(R, T) extra degrees of freedom are calculated. The effects of the modified structure scalars in the modeling of stars through Weyl, shear and expansion scalar differential equations are investigated. The energy density irregularity factor has been calculated for anisotropic radiating spherical stars with varying Ricci scalar corrections.