Study of Accelerated Expansion of Universe in the framework of $f (R, T )$ Gravity

Abstract: This thesis explores the late-time cosmic acceleration within the framework of $f(R,T)$ gravity, a general relativity modification that incorporates the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$. Motivated by observational evidence for the universe's accelerated expansion and the limitations of Einstein's theory in explaining dark energy, we study exact cosmological solutions using various parametrizations of the deceleration parameter. The analysis includes isotropic and anisotropic models such as Bianchi type I universes with string fluid, bulk viscous matter, and magnetized strange quark matter. Several forms of time-varying deceleration parameters are employed to understand the dynamical behavior of the universe. We also examine finite-time singularities like the Big Rip and discuss their occurrence in both anisotropic and FLRW backgrounds. In addition, the thesis investigates higher-order curvature corrections and geometric modifications, including wormhole solutions, within the $f(R,T)$ formalism. Energy conditions are analyzed to assess the physical plausibility of these models. The overall work aims to provide a coherent and viable description of the universe's evolution under modified gravity theories.