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We present an exactly-solvable model for the suppression of quantum noise atlarge scales on expanding space. The suppression arises naturally in the deBroglie-Bohm pilot-wave formulation of quantum theory, according to which theBorn probability rule has a dynamical origin. For a scalar field on aradiation-dominated background we construct the exact solution for thetime-evolving wave functional and study properties of the associated fieldtrajectories. It is shown that the time evolution of a field mode on expandingspace is mathematically equivalent to that of a standard harmonic oscillatorwith a 'retarded time' that depends on the wavelength of the mode. In the farsuper-Hubble regime the equivalent oscillator evolves over only one Hubbletime, yielding a simple mechanism whereby relaxation to the Born rule can besuppressed on very large scales. We present numerical simulations illustratinghow the expansion of space can cause a retardation of relaxation in thesuper-Hubble regime. Given these results it is natural to expect a suppressionof quantum noise at super-Hubble wavelengths. Such suppression could have takenplace in a pre-inflationary era, resulting in a large-scale power deficit inthe cosmic microwave background.

Mechanism for the suppression of quantum noise at large scales on expanding space