Energy density in expanding universes as seen by Unruh's detector

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.

98.80.Cq
04.62.+v
Unruh effect
energy: density
field theory: scalar
tensor: energy-momentum
Bogolyubov transformation
space-time: expansion

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