Cardy-Verlinde Entropy Formula in the Presence of a General Cosmological State Equation

TL;DR

This paper extends the Cardy-Verlinde entropy formula to universes with a general cosmological equation of state and constant bulk viscosity, showing the formula's robustness and providing numerical estimates of effects on cosmic evolution.

Contribution

It demonstrates that the generalized entropy formula remains valid with bulk viscosity and provides numerical estimates for the scale factor and viscosity effects in a radiation-dominated universe.

Findings

The entropy formula holds with bulk viscosity.

Numerical estimates of scale factor evolution.

Viscosity induces measurable corrections to cosmic expansion.

Abstract

As recently found by Youm [hep-th/0201268], the entropy of the universe will no longer be expressible in the conventional Cardy-Verlinde form if one relaxes the radiation dominance state equation and instead assumes a more general equation of the form p=(\gamma-1)\rho, with \gamma a constant. We show that Youm's generalized entropy formula remains valid when the cosmic fluid is no longer ideal, but is allowed to possess a constant bulk viscosity \zeta. We supply our analysis with some numerical estimates, thus calculating the scale factor a(t) for a k=0 universe, and also calculate via a perturbative expansion in \zeta the magnitude of the viscosity-induced correction to the scale factor if the universe is radiation dominated.