For a flat Universe, $C_P/C_V=-q$ : another coincidence in Cosmology?

TL;DR

This paper explores gravitational thermodynamics in an FLRW universe with dissipation, revealing a universal relation between specific heat ratio and the deceleration parameter, independent of the cosmological model.

Contribution

It demonstrates a novel, model-independent relation between specific heat capacities and the deceleration parameter in cosmology with dissipation.

Findings

The ratio of specific heats equals negative deceleration parameter in flat universe.

The relation is independent of the cosmological model used.

Constraints on equation of state and particle creation rate for stability.

Abstract

This paper deals with gravitational thermodynamics on the dynamical apparent horizon of an FLRW universe with dissipation. The dissipation is assumed to arise due to adiabatic gravitational particle creation. For the thermodynamic study, we consider the Bekenstein-Hawking formalism and also assume a nonzero curvature $\kappa$ for a general study. In particular, we study the unified first law, the generalized second law, and thermodynamic stability in our model. The specific heat capacities are taken into account for the study of thermodynamic stability. Our study reveals a nice result! The ratio of the specific heat capacity at constant pressure and that at constant volume in a flat FLRW universe with dissipation is nothing but the negative of the deceleration parameter. In classical thermodynamics, this ratio is known as the isentropic expansion factor or (for ideal gases) the adiabatic index. A more interesting fact that has come to light is that this relation is independent of the cosmological model used. So, this is actually a generic result in Big Bang Cosmology. We discuss the implications of this result on the evolution of the Universe. Finally, we determine the constraints on the effective equation of state and the particle creation rate which guarantees thermodynamic stability in our model.