  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.
