# Gravitational wave induced baryon acoustic oscillations

### Submission summary

 As Contributors: Matthias Bartelmann · Christian Döring Arxiv Link: https://arxiv.org/abs/2107.10283v1 (pdf) Date submitted: 2021-07-30 09:27 Submitted by: Döring, Christian Submitted to: SciPost Physics Academic field: Physics Specialties: Gravitation, Cosmology and Astroparticle Physics Approaches: Theoretical, Phenomenological

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2107.10283v1 on 30 July 2021

## Reports on this Submission

### Strengths

1) This paper studies a new idea, namely to investigate the effects of a background of gravitationla waves on density fluctuations.
2) The calculations are presented in detail and with clarity.
3) The results and their importance is presented clearly.

### Weaknesses

1) There are many formulas which can also be found elsewhere and render the paper very long and tiresome to read.
2) I am not totally convincved that the $\Delta\sigma$ terms in eq. (100) are so much smaller than the \sigma^2 term. Especially as they grow with decreasing redshift when $\Delta$ becomes close to 1.
3) In the late time power spectrum which is observed in galaxy surveys, non-lineairities are important and these may very well 'wash out' the small signal from GWs. This should at leasrt be briefly discussed.

### Report

The paper is in general well written and of good quality. The results are original and interesting. After my requested changes below are considered I recommend the paper for publication.

### Requested changes

1) Give an estimate of the e $\Delta\sigma$ term at late times.
2) Most of section 2 is standard and can be found in text books. I recommend to put this section into an appendix and streamline the main trext.
3) In section 3, assumption 2 you neglect anisotropic stresses also at second order. Please comment why you may neglect the term $\rho v_av_b$ which woul contribute an isotropic stress.
4) $\kappa_{\rm eff}$ in Eq. (117) is not defined.
5) Om p26 'comoving derivative', I think you mean the derivative w.r.t conformal time.

• validity: high
• significance: good
• originality: high
• clarity: high
• formatting: excellent
• grammar: good