Trans-Planckian fluctuations and the stability of quantum mechanics

TL;DR

This paper explores how quantum mechanics might deviate at trans-Planckian scales during inflation, potentially affecting the primordial power spectrum and offering testable predictions via cosmic microwave background observations.

Contribution

It introduces a model where quantum equilibrium is unstable at the Planck scale, leading to observable deviations in primordial fluctuations during inflation.

Findings

Quantum nonequilibrium can be generated by a regulator in pilot-wave dynamics.

The model predicts a power excess in the primordial spectrum at high wavenumbers.

Potential observational tests via cosmic microwave background measurements.

Abstract

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.