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

Abstract

In this paper, we study two different cases of inhomogeneous EOS of the form [Formula: see text]. 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.