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

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=(γ-1)ρ, with γa 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 ζ. 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 ζthe magnitude of the viscosity-induced correction to the scale factor if the universe is radiation dominated.

10 pages, LaTeX, no figures

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