Study of cosmic acceleration and relativistic stellar
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Date
2025-07-01
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UMT Lahore
Abstract
This thesis investigates suitable candidates for dark energy by exploring phenomena like cosmic acceleration through cosmological parameters and cosmic coincidence problems by thermodynamical analysis. We consider the fractal universe model with a timelike fractal profile in the flat FRW universe model and check the thermodynamic stability of various dark energy models. These dark energy models include the family of Chaplygin gas models (such as generalized Chaplygin gas, modified Chaplygin gas, generalized cosmic Chaplygin gas, variable modified Chaplygin gas) and parameterized equation of state (Chevallier-Polarski-Linder) model. To check the stability of these models in a fractal framework thermodynamically, we construct a total equation of state parameters for each case. The conditions to check the stability of models depending on some thermodynamic quantities yield three conditions on this parameter. We graphically check the behavior of the equation of state parameter along with the stability of each model. It is concluded that the dark energy models are thermodynamically stable under appropriate choices of model parameters.
In the framework of f(P) gravity, we examine the nature of the cosmological parameters by choosing the different models of f(P) gravity at past, present, and future epochs. It is found that the equation of state parameter leads to quintessence behavior and also its ranges lie within Planck data constraints. The square speed of sound leads to instability in the linear f(P) model while giving stable behavior in the non-linear f(P) model. We study the validity of the generalized second law of thermodynamics and observe that it holds while failing for the non-linear f(P) model, respectively. However, the thermal equilibrium condition holds for both f(P) models.
Moreover, we use deflection angle formalism to study the thermal stability and phase transitions of 4D charged Einstein-Gauss-Bonnet-AdS black hole in the presence of exponential entropy. We examine the phase structure of the black hole through optical aspects by using the elliptic function analysis. We observe that thermal variation of the deflection angle can be used to obtain stable and unstable phases. We also study the Hawking-Page phase transition from the Gibbs free energy optical dependence using exponential corrected entropy. The particular points of the deflection angle yield transition for large black holes and small black holes. Our Gibbs free energy versus deflection angle behavior confirmed that to obtain the critical behavior of AdS black holes the deflection angle can be utilized as a relevant quantity. Thermodynamic geometry of 4D charged Einstein-Gauss-Bonnet-AdS black hole is also discussed in the presence of corrected exponential entropy.