The Relaxion Measure Problem

TL;DR

This paper investigates the implications of relaxing the classical slow roll condition in relaxion models, revealing potential issues with quantum fluctuation dominance and measure ambiguities that challenge the mechanism's viability.

Contribution

It analyzes the consequences of abandoning the slow roll requirement, highlighting measure problem ambiguities and their impact on relaxion stability and universe regions.

Findings

Quantum fluctuations can dominate relaxion dynamics leading to problematic universe regions.

The measure problem affects the interpretation of the size and significance of these regions.

Using the scale factor cut-off measure, dangerous regions become negligible.

Abstract

We examine the necessity of requiring that relaxion dynamics is dominated by classical slow roll and not quantum fluctuations. It has been recently proposed by Nelson and Prescod-Weinstein that abandoning this requirement can lead to a unified solution of the hierarchy and strong CP problems in QCD relaxion models. In more general models this results in a higher value of the allowed cut-off. In this work we find, however, that relaxing this condition and can result in the universe being dominated in physical volume by regions arising from large quantum fluctuations of the relaxion. These regions turn out to be problematic for the relaxion mechanism because either the relaxion does not stabilise at all or it stabilises at vacua which cannot reproduce the observed properties of our universe. The size of these undesirable regions is moreover ambiguous because of the measure problem. For instance, we show that if one chooses to use the scale factor cut-off measure such dangerous regions occupy a negligible volume and these issues do not arise.