Acoustic gravitational waves beyond leading order in bubble over Hubble radius

2025/04/10 by Lorenzo Giombi, Giombi, Lorenzo, Jani Dahl +3 · 9 citations
Earth and Planetary Sciences · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements

paper · pdf · doi:10.48550/arxiv.2504.08037

openalex publication_date 2025/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H_*^-1, i.e. R_*H_* \lesssim O(1). Since the amplitude of the gravitational wave signal increases with R_*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_*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_*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_*H_* ≃ 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.

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Cited by

• Acoustic gravitational waves from primordial curvature perturbations
• Gravitational waves from the sound shell model: direct and inverse phase transitions in the early Universe
• Vacuum bubbles from cosmic ripples
• Analytic derivation of GW spectrum from bubble collisions in FLRW Universe
• Maximal GW amplitude from bubble collisions in supercooled phase transitions
• Gravitational Waves and Cosmological Observables from First-Order Phase Transitions: Thermal Corrections at Low Temperature

Related

• Numerical simulations of acoustically generated gravitational waves at a first order phase transition
• Characterization of the gravitational wave spectrum from sound waves within the sound shell model
• Signatures of the speed of sound on the gravitational wave power spectrum from sound waves
• Gravitational waves from super-Hubble bubbles
• Acoustic gravitational waves from primordial curvature perturbations