Accelerated detectors and temperature in (anti-) de Sitter spaces

We show, in complete accord with the usual Rindler picture, that detectors with constant acceleration ct 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) = a(5), the detector '5-acceleration' in the embedding fiat 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 wavefunctions in AdS backgrounds.