Accelerated Expansion of the Universe in Nonmetricity-based Modified Gravity

This thesis explores the cosmological implications of modified gravity, focusing on nonmetricity-based $f(Q)$ gravity as an alternative to the $\Lambda$CDM model in explaining cosmic acceleration. Chapter I lays the theoretical groundwork by reviewing General Relativity (GR), $\Lambda$CDM, and the limitations of the standard model, motivating $f(Q)$ gravity. Chapter II constructs cosmological reconstructions of $f(Q)$ gravity within the FLRW framework, deriving forms of $f(Q)$ that replicate the $\Lambda$CDM expansion and using the e-folding parameter to show compatibility with various cosmic histories. Chapter III addresses challenges with arbitrary $f(Q)$ forms by applying Gaussian Process (GP) reconstruction using observational Hubble data. This model-independent method reconstructs the Hubble parameter H(z), leading to a data-driven $f(Q)$ form. Motivated by this, a new parametrization $f(Q) = -2\Lambda + \epsilon Q^2$ is proposed, and power-law and exponential models are tested for consistency. Chapter IV incorporates a quintessence scalar field in power-law $f(Q)$ gravity to study inflation and late-time acceleration. Using GP, the scalar potential $V(\phi)$ is reconstructed and analyzed. Results show that early dark energy has little impact today, but reconstructed quintessence models offer insights into cosmic acceleration. Chapter V examines interacting dark energy and matter under power-law $f(Q)$ using dynamical systems. Two interaction types are studied, and fixed points linked to de Sitter and quintessence solutions are identified. Chapter VI concludes and suggests future work.