  We present an exactly-solvable model for the suppression of quantum noise at
large scales on expanding space. The suppression arises naturally in the de
Broglie-Bohm pilot-wave formulation of quantum theory, according to which the
Born probability rule has a dynamical origin. For a scalar field on a
radiation-dominated background we construct the exact solution for the
time-evolving wave functional and study properties of the associated field
trajectories. It is shown that the time evolution of a field mode on expanding
space is mathematically equivalent to that of a standard harmonic oscillator
with a 'retarded time' that depends on the wavelength of the mode. In the far
super-Hubble regime the equivalent oscillator evolves over only one Hubble
time, yielding a simple mechanism whereby relaxation to the Born rule can be
suppressed on very large scales. We present numerical simulations illustrating
how the expansion of space can cause a retardation of relaxation in the
super-Hubble regime. Given these results it is natural to expect a suppression
of quantum noise at super-Hubble wavelengths. Such suppression could have taken
place in a pre-inflationary era, resulting in a large-scale power deficit in
the cosmic microwave background.
