Gravitational wave induced baryon acoustic oscillations

TL;DR

This paper investigates how gravitational waves from early universe phase transitions influence structure formation, deriving bounds on their properties based on their impact on the matter power spectrum and cosmic variance.

Contribution

It provides a second order perturbation analysis linking gravitational wave energy density from phase transitions to baryon acoustic oscillations, establishing new constraints on phase transition parameters.

Findings

Long-lasting phase transitions can significantly affect matter power spectrum.

Cosmic variance bounds restrict the duration and strength of such phase transitions.

Effects are prominent only for late phase transitions with substantial supercooling.

Abstract

We study the impact of gravitational waves originating from a first order phase transition on structure formation. To do so, we perform a second order perturbation analysis in the $1+3$ covariant framework and derive a wave equation in which second order, adiabatic density perturbations of the photon-baryon fluid are sourced by the gravitational wave energy density during radiation domination and on sub-horizon scales. The scale on which such waves affect the energy density perturbation spectrum is found to be proportional to the horizon size at the time of the phase transition times its inverse duration. Consequently, structure of the size of galaxies and bigger can only be affected in this way by relatively late phase transitions at $\ge 10^{6}\,\text{s}$. Using cosmic variance as a bound we derive limits on the strength $\alpha$ and the relative duration $(\beta/H_*)^{-1}$ of phase transitions as functions of the time of their occurrence which results in a new exclusion region for the energy density in gravitational waves today. We find that the cosmic variance bound forbids only relative long lasting phase transitions, e.g. $\beta/H_*\lesssim 6.8$ for $t_*\approx 5\times10^{11}\,\text{s}$, which exhibit a substantial amount of supercooling $\alpha>20$ to affect the matter power spectrum.