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.
Highlights
The relaxion mechanism, proposed by Graham, Kaplan and Rajendran (GKR) [1], presents a third way of addressing the electroweak hierarchy problem that uses neither symmetries nor anthropics
The subtleties arise after the inflaton stabilizes when some of the above regions expand exponentially because they have a high energy density. This exponential expansion can potentially compensate for the initial exponential suppression if the so-called quantum vs classical (QvsC) requirement is not imposed. To know whether this can spoil the relaxion mechanism, one needs to compute ratio of the volume where the relaxion dynamics successfully explains a small weak scale to the volume generated by these large fluctuations where this might not be achieved
Clearly the second line in Eq (27) is greater than unity for a large enough tc. For this case using the proper time cutoff measure we find that the Nelson and Prescod-Weinstein (NP) model predicts that the number of patches where the relaxion stabilizes in the vacua near φj are exponentially larger than the patches where the relaxion stabilizes in the Σ region
Summary
The relaxion mechanism, proposed by Graham, Kaplan and Rajendran (GKR) [1], presents a third way of addressing the electroweak hierarchy problem that uses neither symmetries nor anthropics. As we discuss in the present work allowing such large quantum fluctuations of the relaxion field can be problematic This is despite the fact that regions where the relaxion spreads far from its classical (expectation) value can be shown to be exponentially small in volume during inflation. This exponential expansion can potentially compensate for the initial exponential suppression if the so-called quantum vs classical (QvsC) requirement is not imposed To know whether this can spoil the relaxion mechanism, one needs to compute ratio of the volume where the relaxion dynamics successfully explains a small weak scale (and in the case of the NP model a small θQCD) to the volume generated by these large fluctuations where this might not be achieved. In particular we confirm the suggestion of NP that these problems do not arise if one uses the scale-factor cutoff measure
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