Qualitative Analysis of Cosmological Models Using Dynamical System Perspective

Abstract

This thesis investigates theoretical and observational aspects of cosmic acceleration, focusing on dark energy models and modified gravity frameworks. The goal is to analyse their viability, dynamical behaviour, and perturbative stability to identify models capable of describing the accelerated expansion of the Universe. Chapter 1 reviews the essential background General Relativity, and mathematics of teleparallel and symmetric teleparallel geometries, basic cosmological models, matter components, and the key observational probes. The chapter concludes with a summary of modified gravity theories, including f(R), f(T) and f(Q). Chapter 2 studies a dissipative Chaplygin gas cosmology in f(Q) gravity. The model is constrained using the CC and Pantheon+SH0ES dataset, and its performance is assessed through information criteria and diagnostic tools such as Om and statefinder analysis. Chapter 3 reconstructs the dynamics of Dirac-Born-Infeld (DBI) dark energy using Hubble and DESI observations via Gaussian Processes. The reconstructed potential is fitted to theoretical models using chi-square and MCMC techniques, giving constrains on DBI scalar field. Chapter 4 analyses canonical scalar-field cosmology in coincident f(Q) gravity using dynamical systems. Chapter 5 extends the dynamical analysis to the DBI scalar field in f(Q) gravity. Chapter 6 examines scalar-field evolution at both background and perturbation levels. Perturbation equations for key gauge invariant variables are derived, and an extended phase space combining background and perturbation dynamics is constructed. Finally, chapter 7 summarizes the main results along with scope for future research. Further mathematical details including derivation of field equation and cosmology equations and foundational issues related to f(Q) gravity are compiled in the following four sections: Appendix A, Appendix B, Appendix C and Appendix D.