The Self-Gravitational Corrections as the Source for Stiff Matter on the Brane in $SAdS_5$ Bulk

TL;DR

This paper investigates how self-gravitational corrections in a five-dimensional Schwarzschild anti-de Sitter bulk influence brane cosmology, revealing an emergent stiff matter component from quantum effects rather than black hole charge.

Contribution

It introduces a novel derivation of self-gravitational corrections to the Friedmann equation using AdS/CFT, showing these effects produce stiff matter on the brane.

Findings

Self-gravitational corrections add a term proportional to a^{-6} in the Hubble equation.

The corrections act as a source of stiff matter, differing from charge-induced effects.

Quantum effects can influence brane cosmology significantly.

Abstract

A $D3-$ brane with non-zero energy density is considered as the boundary of a five dimensional Schwarzschild anti de Sitter bulk background. Taking into account the semi-classical corrections to the black hole entropy that arise as a result of the self-gravitational effect, and employing the AdS/CFT correspondence, we obtain the self-gravitational correction to the first Friedmann-like equation. The additional term in the Hubble equation due to the self-gravitational effect goes as $a^{-6}$. Thus, the self-gravitational corrections act as a source of stiff matter contrary to standard FRW cosmology where the charge of the black hole plays this role.