Dynamical and Cosmological Perspectives on Symmetric Teleparallel Gravity and its Extensions

Abstract

This thesis investigates the late-time accelerated expansion of the Universe within modified gravity theories, with particular emphasis on symmetric teleparallel gravity and its extensions, including $f(Q)$, $f(Q, B)$, and $f(Q, ϕ)$ gravity. It explores the cosmological dynamics of these theories using dynamical systems analysis, stability techniques, and the Noether symmetry approach. The study examines the existence and stability of cosmological critical points, background evolution, and linear cosmological perturbations to understand the different phases of cosmic evolution. It also investigates the role of observational constraints and Big Bang nucleosynthesis in assessing the viability of modified gravity models. Furthermore, the application of Noether symmetries provides a systematic approach to identifying viable functional forms and deriving exact cosmological solutions. Overall, this thesis examines the theoretical and cosmological viability of modified teleparallel gravity as an alternative framework for describing the observed accelerated expansion of the Universe.