Energy conditions for Inhomogeneous EOS and its Thermodynamics analysis with the resolution on finite time future singularity problems

TL;DR

This paper investigates inhomogeneous equations of state in cosmology, analyzing energy densities, singularities, and thermodynamic stability, providing insights into finite-time future singularities and thermodynamics of dark fluids.

Contribution

It introduces new models of inhomogeneous EOS, derives their energy densities, and examines their thermodynamic stability and singularity resolution.

Findings

Energy densities are explicitly derived for both EOS cases.

Finite time singularities are analyzed and addressed.

Thermodynamic stability conditions are satisfied for both models.

Abstract

In this paper we study two different cases of inhomogeneous EOS of the form p_d = \omega(t)\rho_d+w_1 f(H, t) . We derive the energy density of dark fluid and dark matter component for both the cases. Further we calculate the evolution of energy density, gravitational constant and cosmological constant. We also explore the finite time singularity and thermodynamic stability conditions for the two cases of EOS. Finally, we discuss the thermodynamics of inhomogeneous EOS with the derivation of internal energy, Temperature and entropy and also show that all the stability conditions are satisfied for the two cases of EOS