Accelerating Expansion of the Universe in modified gravity with quadratic terms

Chapter1 introduces cosmic acceleration and outlines key features and limitations of GR and its alternatives, including teleparallel and symmetric teleparallel gravity. In Chapter2, we analyze the cosmological implications of $f(T,\mathcal{T})$ theory by considering the squared-torsion model $f(T,\mathcal{T})= \alpha \mathcal{T}+ \beta T^2$, where $T$ represents torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor. In Chapter3, we explore the inflationary scenario within the framework of torsion-trace coupling gravity, utilizing a Lagrangian density derived from a function denoted as $f(T,\mathcal{T})$. In Chapter4, we aim to investigate the dark sector of the Universe, which encompasses the enigmatic components of the Dark Matter (DM) and Dark Energy (DE). We consider an extended form of the Equation of State (EoS) for DM, widely known as the Extended Bose-Einstein Condensation (EBEC) EoS for DM. In Chapter5, we propose an extended formulation of symmetric teleparallel gravity by generalizing the gravitational Lagrangian through the inclusion of an arbitrary function of $f(Q,\mathcal{T_{\mu\nu}} \mathcal{T^{\mu\nu}})$. We derived the FRW equations for a flat, homogeneous, and isotropic spacetime. In Chapter6, we delved into the dark sector of the Universe, specifically focusing on DM and DE. We examine an extended version of the EoS for DM, commonly referred to EBEC EoS for DM, given as $p=\alpha \rho + \beta \rho^2$, alongside the modified $f(Q)$ Lagrangian given by $f(Q)= \gamma Q^2$.