Accelerated Detectors and Temperature in (Anti) de Sitter Spaces

TL;DR

This paper demonstrates that accelerated detectors in de Sitter and Anti de Sitter spaces measure a temperature related to their acceleration and the cosmological constant, confirming the thermal nature of the spectrum in these curved spacetimes.

Contribution

It provides a unified formula for the temperature measured by detectors in (A)dS spaces based on their acceleration and the cosmological constant, extending known results and analyzing the AdS case.

Findings

Detectors in (A)dS spaces measure temperature proportional to their acceleration and cosmological constant.

The temperature formula is valid down to zero acceleration in AdS, consistent with spacetime kinematics.

A thermal spectrum is confirmed for various wave functions in AdS backgrounds.

Abstract

We show, in complete accord with the usual Rindler picture, that detectors with constant acceleration $a$ in de Sitter (dS) and Anti de Sitter (AdS) spaces with cosmological constants $\Lambda$ measure temperatures $2\pi T=(\Lambda/3+a^{2})^{1/2}\equiv a_{5}$, the detector "5-acceleration" in the embedding flat 5-space. For dS, this recovers a known result; in AdS, where $\Lambda$ is negative, the temperature is well defined down to the critical value $a_{5}=0$, again in accord with the underlying kinematics. The existence of a thermal spectrum is also demonstrated for a variety of candidate wave functions in AdS backgrounds.