Cosmological Solutions of Modified Theories of Gravity

Abstract

This thesis presents a comprehensive study of various cosmological models formulated newlinewithin the framework of modified theories of gravity, constrained by the newlinelatest observational datasets. In Chapter 2, a plane symmetric cosmological model newlinewith quark and strange quark matter is investigated using f(R, T) gravity. By applying newlinea power-law relation and a variable deceleration parameter, and analyzing newline57 observational data points of the Hubble parameter, we obtained a best-fit value newlineof H0 = 64.39 km/s/Mpc, with R2 = 0.9321 and RMSE = 11.0716, demonstrating newlineclose agreement with the CDM model. newlineChapter 3 explores a Bianchi Type-V universe embedded with a magnetized newlinedomain wall in f(R, T) gravity. Themodel, constrained by the same observational newlinedataset, shows strong consistency with CDM, with H0 = 68.45 km/s/Mpc, R2 = newline0.9280, and RMSE = 11.400. Om diagnostics and the jerk parameter further newlinevalidate its depiction of the universe s accelerating expansion. newlineIn Chapter 4, we turn to Bianchi Type-I cosmological models within f(T) newlinegravity, incorporating heat flow. Exact solutions are derived, and cosmological newlineparameters are expressed in terms of redshift, o!ering a meaningful connection newlinebetween theory and observation. Chapter 5 introduces a cubic parametrization of newlinethe deceleration parameter within the f(T) framework. The model, constrained newlineby data, yields excellent agreement with observations R2 = 0.9527 and captures newlinethe universe s transition from deceleration to acceleration. Statefinder and Om newlinediagnostics reinforce the model s reliability. newlineFinally, Chapter 6 investigates a parameterized Hubble function in fractal gravity, newlineemploying least squares fitting on Hubble and Pantheon datasets. A transition newlinepoint between deceleration and acceleration is identified within 0.5 and#8593; zda and#8593; 1.668, newlinesupported by analyses of pressure, energy density, and energy conditions. Collectively, newlinethese studies o!er valuable insights into the dynamics of cosmic evolution newlineand support the potential of modified gravity theories as compelling alternatives newlinet