Study of Cosmic Acceleration and Thermodynamic Consequences in Alternative Theories of Gravity

Abstract

In this thesis, we discuss two interesting issues: the accelerated expansion of the universe and thermodynamics. We consider flat Friedmann-Robertson-Walker universe model in alternative theories of gravity like loop quantum cosmology, Dvali- Gabadaze-Porrati brane world and fractal universe. We use different models of dark energy like Ricci Gauss-Bonnet dark energy and some latest holographic dark energy models namely Tsallis, Renyi and Sharma-Mittal holographic dark energy models for the analysis of both issues. For accelerated expansion of the universe, we examine the cosmological parameters like effective equation of state parameter, deceleration parameter, statefinder parameters, Om-diagnostic, plane of effective equation of state parameter with its evolutionary parameter and squared speed of sound parameter. We investigate the validity of the generalized second law of thermodynamics and thermodynamical equilibrium for the case of thermodynamic analysis. Firstly, we consider loop quantum cosmology and fractal universe in flat FRW universe with an interacting scenario between a non-canonical scalar field model of dark energy and dark matter. We make the analysis by using constant and variable (CPL parametrization) forms of equation of state parameters. We discuss the deceleration parameter for expansion rate along with squared speed of sound for stability analysis. Taking Bekenstein, logarithmic and power law entropies as the horizon entropy, we examine generalized second law of thermodynamics and thermal equilibrium. Secondly, we study the cosmological implications using Tsallis, Renyi and Sharma- Mittal holographic dark energy models in the interacting framework. We take into account two theories, fractal and Dvali-Gabadaze-Porrati brane world. We discuss the cosmological parameters and planes in both theories for the evolving universe. Finally, we examine the validity of generalized second law of thermodynamics of a physical system enveloped by apparent as well as event horizons. The system is comprised of Ricci Gauss-Bonnet dark energy and dark matter. We use various forms of entropy namely Bekenstein, Renyi, logarithmic and power law entropy corrections. We also examine the thermodynamic equilibrium in case of each entropy.