  We present arguments suggesting that deviations from the Born probability
rule could be generated for trans-Planckian field modes during inflation. Such
deviations are theoretically possible in the de Broglie-Bohm pilot-wave
formulation of quantum mechanics, according to which the Born rule describes a
state of statistical equilibrium. We suggest that a stable equilibrium state
can exist only in restricted conditions: on a classical background spacetime
that is globally hyperbolic or in a mild quantum-gravity regime in which there
is an effective Schr\"odinger equation with a well-defined time parameter.
These arguments suggest that quantum equilibrium will be unstable at the Planck
scale. We construct a model in which quantum nonequilibrium is generated by a
time-dependent regulator for pilot-wave dynamics, where the regulator is
introduced to eliminate phase singularities. Applying our model to
trans-Planckian modes that exit the Planck radius, we calculate the corrected
primordial power spectrum and show that it displays a power excess (above a
critical wavenumber). We briefly consider how our proposals could be tested by
measurements of the cosmic microwave background.
