Thermodynamical Aspects of Some Cosmological Models

Duary, Tanima (2024) Thermodynamical Aspects of Some Cosmological Models. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

This thesis is focused on the thermodynamic analysis of cosmological models, specially the models that explain late-time cosmic acceleration. The cosmological principle says that the universe exhibits spatial homogeneity and isotropy. To describe it we consider the Friedmann-Lemaître-Robertson- Walker (FLRW) metric. A thorough evaluation of the feasibility of the models was conducted through the application of the Generalized Second Law (GSL). This law says that the overall entropy, i.e., the sum of the entropy of the horizon and the fluid enclosed within the horizon, should never decrease. Considering the dynamic nature of the universe, our methodology focused on the apparent horizon, instead of the event horizon. Within this framework, we have considered a condition of thermodynamic equilibrium between the apparent horizon and the fluid contained within it. In this state of equilibrium, we have considered the Hayward-Kodama temperature as the temperature associated with the apparent horizon. The first chapter contains concise overview of cosmology. Chapter 2 goes deeper into the thermodynamics applied to cosmology. It focuses more on the Generalized Second Law of Thermodynamics and explains it in more detail. Furthermore, we go into extensive details regarding Hayward-Kodama temperature. This chapter also contains a detail discussion about apparent horizon. The conditions required for thermodynamic stability has been discussed in this chapter. In chapter 3, we conduct a thermodynamic comparison between quintessence models involving thawing and freezing scenarios. We have considered an ansatz on the energy density of the scalar field, which is picked up from the literature. The motivation for picking the ansatz was that, by choosing values of just one parameter, we can get either thawing or freezing behaviour. Both of these models are observed to violate the Generalized Second Law of Thermodynamics. Nevertheless, in the case of freezing models, there is still a possible way to resolve this, as this violation occurs in the distant past, deep within the radiation-dominated era, a period where a conventional scalar field model combined with pressureless matter is not an accurate representation of the matter content. In contrast, the thawing model exhibits a violation of GSL, manifesting as a finite future breakdown. Therefore, we conclude that the freezing models are favoured compared to the thawing ones on the considerations of GSL viability. In chapter 4, we scrutinize Brans-Dicke cosmological models within the context of a spatially isotropic and homogeneous universe, evaluating their compatibility with the GSL. Our investigation is carried out within the Einstein frame. We find that in dust era, these models exhibit thermodynamic feasibility when the Brans-Dicke parameter w assumes negative values. This range has strong alignment with the range that is required for the recent observations of the cosmic acceleration. In chapter 5, we explore the thermodynamic viability of a selection of dark energy models, which have been reconstructed using the cosmological jerk parameter. Our investigation involves the adoption of models previously documented in the literature. These models are categorized into two groups based on the presence or absence of interactions in the dark sector. We employ the GSL as a diagnostic tool for our analysis. In an attempt to capture the dynamic nature of spacetime, we replace the Hawking temperature with the Hayward-Kodama temperature. Our results indicate that, dependent on the chosen parametrization ansatz for jerk, the total entropy exhibits a time-increasing trend. This suggests the potential existence of viable models within this framework. This trend persists even when there is interaction in the dark sector. In chapter 6, we have considered a model in spatially flat FRWspacetime, that mimics the characteristics of LCDM model and checked the thermodynamic stability. In this chapter also we have utilized the Hayward-Kodama temperature as the temperature of the apparent horizon. Assuming the thermal equilibrium between the apparent horizon and the fluid inside the horizon, we investigated the thermodynamic stability of the matter composition within the universe and found out that it lacks the thermodynamic stability. We found out an interesting result while calculating the heat capacity at constant volume (CV). It is shown that the transition from the decelerated to the accelerated cosmic expansion is a second-order thermodynamic phase transition, while the deceleration parameter q serves as the order parameter. In chapter 7, we reach the epilogue of this thesis, where we not only provide our final conclusions but also briefly discussed the aspects of the work presented in this dissertation and future prospects.

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