Gravitational waves from bubble collisions: analytic derivation

TL;DR

This paper derives an analytic method to estimate gravitational wave spectra from bubble collisions during cosmological phase transitions, simplifying previous simulation-based approaches and revealing key spectral features.

Contribution

It presents an analytic derivation of gravitational wave spectra from bubble collisions, improving upon prior simulation methods under thin-wall and envelope approximations.

Findings

Most contributions to the spectrum come from single-bubble effects.

The high-frequency fall-off of the spectrum is proportional to f^{-1}.

Provided fitting formulas for the gravitational wave spectrum.

Abstract

We consider gravitational wave production by bubble collisions during a cosmological first-order phase transition. In the literature, such spectra have been estimated by simulating the bubble dynamics, under so-called thin-wall and envelope approximations in a flat background metric. However, we show that, within these assumptions, the gravitational wave spectrum can be estimated in an analytic way. Our estimation is based on the observation that the two-point correlator of the energy-momentum tensor $\langle T(x)T(y)\rangle$ can be expressed analytically under these assumptions. Though the final expressions for the spectrum contain a few integrations that cannot be calculated explicitly, we can easily estimate it numerically. As a result, it is found that the most of the contributions to the spectrum come from single-bubble contribution to the correlator, and in addition the fall-off of the spectrum at high frequencies is found to be proportional to $f^{-1}$. We also provide fitting formulae for the spectrum.