Gravity Waves from a Cosmological Phase Transition: Gauge Artifacts and Daisy Resummations

TL;DR

This paper investigates how gauge choices and higher-order resummations affect predictions of gravitational wave spectra from cosmological phase transitions, highlighting significant impacts on theoretical accuracy.

Contribution

It demonstrates the substantial gauge dependence in gravitational wave predictions and evaluates the effects of daisy resummations using a gauge-invariant formalism in a simple model.

Findings

Gauge choice dramatically affects gravity wave spectrum predictions.

Resumming higher-order contributions can reduce the spectrum amplitude by over an order of magnitude.

Gauge-invariant approaches are crucial for reliable predictions in cosmological phase transition models.

Abstract

The finite-temperature effective potential customarily employed to describe the physics of cosmological phase transitions often relies on specific gauge choices, and is manifestly not gauge-invariant at finite order in its perturbative expansion. As a result, quantities relevant for the calculation of the spectrum of stochastic gravity waves resulting from bubble collisions in first-order phase transitions are also not gauge-invariant. We assess the quantitative impact of this gauge-dependence on key quantities entering predictions for gravity waves from first order cosmological phase transitions. We resort to a simple abelian Higgs model, and discuss the case of R_xi gauges. By comparing with results obtained using a gauge-invariant Hamiltonian formalism, we show that the choice of gauge can have a dramatic effect on theoretical predictions for the normalization and shape of the expected gravity wave spectrum. We also analyze the impact of resumming higher-order contributions as needed to maintain the validity of the perturbative expansion, and show that doing so can suppress the amplitude of the spectrum by an order of magnitude or more. We comment on open issues and possible strategies for carrying out "daisy resummed" gauge invariant computations in non-Abelian models for which a gauge-invariant Hamiltonian formalism is not presently available.