Theoretical uncertainties for cosmological first-order phase transitions

TL;DR

This paper analyzes the theoretical uncertainties in calculating first-order phase transitions relevant to gravitational wave predictions, highlighting the impact of different perturbative methods on the reliability of these calculations.

Contribution

It compares traditional daisy resummation with dimensional reduction, showing the latter reduces uncertainties and improves gauge invariance in phase transition calculations.

Findings

Large uncertainties in gravitational wave amplitude predictions with daisy resummation.

Dimensional reduction significantly reduces scale dependence and enhances gauge invariance.

The improved approach addresses key issues in perturbative calculations of phase transitions.

Abstract

We critically examine the magnitude of theoretical uncertainties in perturbative calculations of first-order phase transitions, using the Standard Model effective field theory as our guide. In the usual daisy-resummed approach, we find large uncertainties due to renormalisation scale dependence, which amount to two to three orders-of-magnitude uncertainty in the peak gravitational wave amplitude, relevant to experiments such as LISA. Alternatively, utilising dimensional reduction in a more sophisticated perturbative approach drastically reduces this scale dependence, pushing it to higher orders. Further, this approach resolves other thorny problems with daisy resummation: it is gauge invariant which is explicitly demonstrated for the Standard Model, and avoids an uncontrolled derivative expansion in the bubble nucleation rate.