  In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we
develop field-theoretical models of quantum nonequilibrium systems which could
exist today as relics from the very early universe. We consider relic excited
states generated by inflaton decay, as well as relic vacuum modes, for particle
species that decoupled close to the Planck temperature. Simple estimates
suggest that, at least in principle, quantum nonequilibrium could survive to
the present day for some relic systems. The main focus of this paper is to
describe the behaviour of such systems in terms of field theory, with the aim
of understanding how relic quantum nonequilibrium might manifest
experimentally. We show by explicit calculation that simple perturbative
couplings will transfer quantum nonequilibrium from one field to another (for
example from the inflaton field to its decay products). We also show that
fields in a state of quantum nonequilibrium will generate anomalous spectra for
standard energy measurements. Possible connections to current astrophysical
observations are briefly addressed.
