Understanding thermal nature of de Sitter spacetime via inter-detector interaction

Abstract

We investigate the interaction potential of two static detectors (atoms) at the same radial but different azimuthal coordinates in the de Sitter invariant vacuum. We show that for two detectors very far away from the cosmological horizon, the interaction potential is different from that of two static ones in a thermal bath in Minkowski spacetime at a temperature equal to the Gibbons-Hawking temperature, suggesting that de Sitter spacetime in regard to its thermal nature basically differs from a thermal bath in Minkowski spacetime. For two detectors very close to the cosmological horizon, the interaction potential behaves as ∼[TUρ4ln⁡(4TUρ)]−1 with TU and ρ the Unruh temperature associated with the proper acceleration and the proper separation of the detectors, which deviates dramatically from ∼(TUρ4)−1, the behavior of the interaction potential of two synchronously uniformly accelerated detectors in Minkowski spacetime, indicating that thermal nature of de Sitter spacetime also differs essentially from the Unruh thermal bath.