Cosmological and Dynamical Instability Analysis in Some Modified Theories of Gravity

Abstract

The present thesis comprises the study of three dynamical phenomena such as evolution of the universe through cosmological parameters, thermodynamics via the generalized second law of thermodynamics and dynamical instability of collapsing star taking into account adiabatic index. Firstly, we consider a new holographic dark energy model in the framework of dynamical Chern-Simons modified theory of gravity to explore various cosmological parameters (like equation of state, squared speed of sound, Om-diagnostic) and cosmological planes ( d d  ' where d ' is the evolutionary equation of state parameter, statefinders). We examine their graphical results and also comprise with the different observational data like Planck, 0 H , SNLS and WMAP. Secondly, the thermodynamics through generalized second law of thermodynamics in the framework of dynamical Chern-Simons theory of gravity by taking interaction between dark energy and dark matter is discussed. In the first part, we discuss the scalar field phenomenon of dark energy model having a non-canonical kinetic term in the flat universe and investigate the stability of the model through squared speed of sound. The generalized second law of thermodynamics by taking usual entropy and its correction forms like logarithmic and power law at apparent horizon is studied. In second part, this law is investigated by taking the interaction of dark matter and dark energy with holographic dark energy model and different cutoffs like Hubble horizon, event horizon, their combination, Ricci scalar and its generalized form. The generalized form of second law of thermodynamics in terms of coincidence parameter is being evolved. Next, we choose the framework of modified Brans-Dicke gravity to study generalized second law of thermodynamics by developing the expressions tot S ' for usual entropy as well as its corrected forms, logarithmic and power law corrected on the apparent and event horizons. Also, the power law forms of scalar field and scale factor are utilized in order to analyze the clear view of thermodynamic law. Finally, we find the instability ranges of spherical and cylindrical symmetric structures of a collapsing object in FT, theory where, T denotes the torsion scalar and  is the trace of energy-momentum tensor. The perturbation method is used upto first order in the modified field equations to construct dynamical collapse equations. These equations with adiabatic index are utilized to check the instability ranges in Newtonian and post-Newtonian limits. It is found that the instability ranges depend on the dynamical variables of collapsing object.