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

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) ≡ 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 wavefunctions in AdS backgrounds.