Unruh effect for a Dvali-Gabadadze-Porrati Brane

TL;DR

This paper investigates the Unruh effect for a Dvali-Gabadadze-Porrati (DGP) brane, revealing how the perceived temperature relates to brane acceleration, matter density, and the influence of extra dimensions in braneworld cosmology.

Contribution

It provides a detailed analysis of the Unruh temperature in DGP branes, including conditions where it equals the geometric temperature and effects of matter content.

Findings

Unruh temperature is proportional to brane acceleration.

Unruh temperature remains non-zero even as the 5th dimension's gravitational effect vanishes.

Unruh temperature equals geometric temperature in specific matter and curvature conditions.

Abstract

In braneworld cosmology the brane accelerates in the bulk, and hence it perceives Unruh radiations in the bulk. We discuss the Unruh effect for a Dvali-Gabadadze-Porrati (DGP) brane. We find that the Unruh temperature is proportional to the acceleration of the brane, but chemical potential appears in the distribution function for massless modes. The Unruh temperature does not vanish even at the limit $r_c\to \infty$, which means the gravitational effect of the 5th dimension vanishes. The Unruh temperature equals the $geometric$ temperature when the the density of matter on the brane goes to zero for branch $\epsilon=1$, no matter what the value of the cross radius $r_c$ and the spatial curvature of the brane take. And if the state equation of the matter on the brane satisfies $p=-\rho$, the Unruh temperature always equals the geometric temperature of the brane for both the two branches, which is also independent of the cross radius and the spatial curvature. The Unruh temperature is always higher than geometric temperature for a dust dominated brane.