Quantum bounds for gravitational de Sitter entropy and the Cardy-Verlinde formula

TL;DR

This paper investigates quantum corrections to the Cardy-Verlinde entropy formula in cosmological and de Sitter spaces, showing that these corrections can be incorporated via an effective cosmological constant, supporting the formula's universality.

Contribution

It demonstrates how quantum effects can be integrated into the Cardy-Verlinde formula through an effective cosmological constant, extending its validity.

Findings

Quantum corrections can be represented by an effective cosmological constant.

The corrected Cardy-Verlinde formula remains valid with quantum effects.

A relation between the Cardy-Verlinde formula and the ADM Hamiltonian constraint is proposed.

Abstract

We analyze different types of quantum corrections to the Cardy-Verlinde entropy formula in a Friedmann-Robertson-Walker universe and in an (anti)-de Sitter space. In all cases we show that quantum corrections can be represented by an effective cosmological constant which is then used to redefine the parameters entering the Cardy-Verlinde formula so that it becomes valid also with quantum corrections, a fact that we interpret as a further indication of its universality. A proposed relation between Cardy-Verlinde formula and the ADM Hamiltonian constraint is given.