Expanding Universe: Thermodynamical Aspects From Different Models

TL;DR

This paper examines the thermodynamical behavior of the universe using two cosmological models, deriving general expressions for energy density, analyzing stability, and validating thermodynamic laws within different horizons.

Contribution

It introduces a generalized expression for energy density applicable to various models and discusses thermodynamic stability and the third law in cosmological contexts.

Findings

Derived a general energy density expression independent of specific models

Analyzed thermodynamic stability conditions for the models

Validated thermodynamic laws within apparent and event horizons

Abstract

The pivotal point of the paper is to discuss the behavior of temperature, pressure, energy density as a function of volume along with determination of caloric EoS from following two model: $w(z)=w_{0}+w_{1}\ln(1+z)$ & $ w(z)=-1+\frac{(1+z)}{3}\frac{A_{1}+2A_{2}(1+z)}{A_{0}+2A_{1}(1+z)+A_{2}(1+z)^{2}}$. The time scale of instability for this two models is discussed. In the paper we then generalize our result and arrive at general expression for energy density irrespective of the model. The thermodynamical stability for both of the model and the general case is discussed from this viewpoint. We also arrive at a condition on the limiting behavior of thermodynamic parameter to validate the third law of thermodynamics and interpret the general mathematical expression of integration constant $U_{0}$ (what we get while integrating energy conservation equation) physically relating it to number of micro states. The constraint on the allowed values of the parameters of the models is discussed which ascertains stability of universe. The validity of thermodynamical laws within apparent and event horizon is discussed.