arXiv:2504.08037v1 Announce Type: new
Abstract: We calculate the gravitational wave power spectrum from sound waves in a cosmological first order phase transition in the unexplored regime of large bubbles, by which we mean that the mean bubble spacing $R_*$ is a non-negligible fraction of the Hubble length $mathcal{H}_*^{-1}$, i.e. $R_*mathcal{H}_* lesssim mathcal{O}(1)$. Since the amplitude of the gravitational wave signal increases with $R_*mathcal{H}_*$, this is also the loud signal regime. In this regime the effects of gravity, hitherto neglected, become relevant. We carry out the calculation in cosmological perturbation theory expanding in the parameter $R_*mathcal{H}_*$, or bubble over Hubble radius. The leading order term is the standard result for acoustic production of gravitational waves. At next-to-leading order we find three novel contributions: two contributions arise from general relativistic corrections to the dynamics of both sound and gravitational waves. A third contribution comes from gravitational waves induced by curvature perturbations. These contributions suppress the gravitational wave peak amplitude. The suppression factor, with respect to the leading order contribution, scales as $(R_*mathcal{H}_*)^2$, and also depends on other transition parameters, such as the sound speed $c_s$, the duration of the acoustic source, and the peak wavenumber of the velocity field $k_p$. In a simplified model of the velocity field, we find that the suppression factor lies between $2%$ and $15%$ when $R_*mathcal{H}_* simeq 0.5$, but is independent of the root mean squared fluid velocity. We provide analytical approximations to the next-to-leading order corrections, and a recipe to join them smoothly across different frequency regimes. Our work improves the precision of the current estimations of the gravitational wave power spectrum in the relatively unexplored regime of phase transition with large bubbles.
Future Roadmap for Readers
Introduction
This article presents a calculation of the gravitational wave power spectrum from sound waves in a cosmological first order phase transition. The focus is on the regime of large bubbles, where the mean bubble spacing is a non-negligible fraction of the Hubble length. The aim of this roadmap is to provide an overview of the conclusions of the study and outline potential challenges and opportunities on the horizon.
Calculation in Cosmological Perturbation Theory
The authors carry out the calculation using cosmological perturbation theory, expanding in the parameter $R_*mathcal{H}_*$, which represents the ratio of bubble spacing to Hubble length. The leading order term corresponds to the standard result for acoustic production of gravitational waves.
Novel Contributions at Next-to-Leading Order
At next-to-leading order, the authors find three novel contributions to the gravitational wave power spectrum. First, there are general relativistic corrections to the dynamics of both sound and gravitational waves. Second, there are gravitational waves induced by curvature perturbations. These contributions result in a suppression of the gravitational wave peak amplitude.
Suppression Factor
The suppression factor, compared to the leading order contribution, scales as $(R_*mathcal{H}_*)^2$ and depends on other transition parameters such as the sound speed, duration of the acoustic source, and peak wavenumber of the velocity field. In a simplified model, the authors find that the suppression factor ranges from 2% to 15% when $R_*mathcal{H}_* simeq 0.5$. Notably, the suppression factor is independent of the root mean squared fluid velocity.
Analytical Approximations and Smooth Frequency Regime Transition
The authors provide analytical approximations to the next-to-leading order corrections, allowing for more precise estimations of the gravitational wave power spectrum in the regime of phase transition with large bubbles. They also propose a recipe to smoothly join the corrections across different frequency regimes.
Conclusion
This study significantly improves the precision of estimations for the gravitational wave power spectrum in cosmological phase transitions with large bubbles. By considering both leading order and next-to-leading order contributions, the authors uncover novel gravitational wave effects and provide valuable insights for future research in this unexplored regime.
Potential Challenges and Opportunities
- Challenges may arise in extending the calculations and approximation techniques to more complex velocity field models.
- Further investigations are needed to explore the impact of additional transition parameters on the gravitational wave power spectrum.
- Opportunities exist for experimental validation of the predictions through gravitational wave observations by upcoming detectors.
- Future research can build upon this work to study the implications of these findings for cosmological models and the early universe.