Viscous Cosmology and the Cardy-Verlinde Formula

TL;DR

This paper explores extending the holographic principle and the Cardy-Verlinde entropy formula to a universe with bulk viscosity, questioning the physical interpretation of Casimir energy and validating a generalized entropy formula.

Contribution

It introduces a generalized entropy formula applicable to viscous cosmic fluids, expanding the holographic principle beyond ideal radiation-dominated universes.

Findings

The Cardy-Verlinde formula can be formally extended to viscous fluids.

The physical interpretation of Casimir energy in viscous cases is problematic.

Youm's generalized entropy formula remains valid with bulk viscosity.

Abstract

The holographic principle in a radiation dominated universe is extended to incorporate the case of a bulk-viscous cosmic fluid. This corresponds to a nonconformally invariant theory. Generalization of the Cardy-Verlinde entropy formula to the viscous case appears to be possible from a formal point of view, although we question on physical grounds the manner in which the Casimir energy is evaluated in this case. Also, we consider an observation recently made by Youm, 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 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.