Accelerated Detectors and Temperature in (Anti) de Sitter Spaces

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 $Λ$ measure temperatures $2πT=(Λ/3+a^{2})^{1/2}\equiv a_{5}$, the detector "5-acceleration" in the embedding flat 5-space. For dS, this recovers a known result; in AdS, where $Λ$ 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.