The Sound of the Universe: A Resonant Gravitational Instability Driven by Baryon-Dark Matter Relative Drift

Abstract

Dark matter and baryons acquire a relative velocity after decoupling in the early Universe. Baryons are gravitationally unstable only above their Jeans scale, while cold dark matter (CDM) is unstable on all scales. We show for the first time that their relative drift triggers a resonant gravitational instability that drives sound waves in baryons. When the projected DM drift is subsonic, the stable oscillatory branch of baryons resonates with the Doppler-shifted DM mode, producing exponentially growing perturbations whose growth rates exceed the intrinsic CDM growth rate. The instability peaks below the baryon Jeans scale and, in baryon-dominated environments, opens a window of complete stability between the Jeans scale and the resonance. Supersonic drift suppresses growth, as previously noted. The resonant coupling also transfers momentum between the species, creating a non-viscous, collisionless drag. We derive an accurate analytical approximation for the growth rate at resonance and show that the associated timescales range from years to tens of millions of years across diverse environments -- planets, protoplanetary disks, stars, molecular clouds, galaxies, and galaxy clusters -- typically much shorter than their ages. In an expanding FLRW universe, the instability enhances baryon density perturbations at different redshifts for appropriately oriented modes while suppressing the growth of those aligned with the DM stream. The universe thus sings across all scales, and this resonant mechanism provides the means to listen: it offers a novel probe of dark matter through its seismic imprint on astrophysical objects and may explain long-standing puzzles such as the persistence of spiral arms and the heating of the intracluster medium in galaxy clusters.