Energy Density in Expanding Universes as Seen by Unruh's Detector

TL;DR

This paper analyzes how Unruh detectors respond to scalar fields in expanding universes, revealing that the detector's response aligns with particle number expectations from stress-energy, challenging previous claims of a thermal spectrum in de Sitter space.

Contribution

It demonstrates that the detector response at second order captures the particle number consistent with stress-energy, contradicting the idea of an exponentially suppressed thermal spectrum in de Sitter space.

Findings

Detector response reproduces particle number from stress-energy.

Second order transition amplitude dominates in the ultraviolet.

Response does not drop exponentially, challenging thermal spectrum assumptions.

Abstract

We consider the response of an Unruh detector to scalar fields in an expanding space-time. When combining transition elements of the scalar field Hamiltonian with the interaction operator of detector and field, one finds at second order in time-dependent perturbation theory a transition amplitude, which actually dominates in the ultraviolet over the first order contribution. In particular, the detector response faithfully reproduces the particle number implied by the stress-energy of a minimally coupled scalar field, which is inversely proportional to the energy of a scalar mode. This finding disagrees with the contention that in de Sitter space, the response of the detector drops exponentially with particle energy and therefore indicates a thermal spectrum.