Viscous Cosmology, Entropy, and the Cardy-Verlinde Formula

TL;DR

This paper extends the holographic principle and Cardy-Verlinde entropy formula to viscous cosmological fluids, analyzing how bulk viscosity affects entropy relations and their physical interpretations in non-conformal theories.

Contribution

It generalizes the Cardy-Verlinde entropy formula to include bulk viscosity, showing the formula's validity beyond ideal fluids and radiation dominance assumptions.

Findings

The generalized entropy formula remains valid with constant bulk viscosity.

Viscous effects modify the evaluation of Casimir energy in the entropy relation.

The paper surveys cosmological models with shear and bulk viscosity.

Abstract

The holographic principle in a radiation dominated universe, as discussed first by Verlinde (2000), is extended so as to incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a non-conformally invariant theory. Generalization of the Cardy-Verlinde entropy formula to the viscous case appears to be formally possible, although on physical grounds one may question some elements in this type of theory, especially the manner in which the Casimir energy is evaluated. Also, we consider the observation made by Youm (2002),namely that the entropy of the universe is no longer expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance equation of state for the fluid and instead merely assumes that the pressure is proportional to the energy density. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but endowed with a constant bulk viscosity. In the introductory part of this article, we take a general point of view and survey the essence of cosmological theory applied to a fluid containing both a constant shear viscosity and a constant bulk viscosity.