Structure Formation with Warm White Noise: Effects of Finite Number Density and Velocity Dispersion in Particle and Wave Dark Matter
arXiv:2503.20881 · doi:10.1088/1475-7516/2026/01/016
Abstract
We investigate the evolution of density perturbations in dark matter, including the new combined effects of finite number density and non-zero velocity dispersion. Using a truncated BBGKY hierarchy, we derive analytical expressions for the dark matter power spectrum during radiation and matter domination. A component of warm white noise emerges in our analysis, which arises due to the finite number density and undergoes scale-dependent evolution because of the velocity dispersion. Although free streaming erases adiabatic initial perturbations on small scales, warm white noise persists below the free-streaming length and grows during matter domination, with growth suppressed below the dark matter Jeans length. Our calculated power spectra agree with -body simulations in the linear regime and accurately predict halo mass functions in the nonlinear regime. Effects of warm white noise can emerge on observable quasi-linear scales for ultralight dark matter produced after inflation with a subhorizon correlation length. Our formalism is applicable to these scenarios (with de Broglie-scale quasi-particles), to cases in which dark matter includes macroscopic structures (such as primordial black holes), and to traditional warm and cold dark matter scenarios.
arXiv comment37 pages+appendices, 15 figures. Accepted by JCAP. Code for numerically evolving the power spectra available at https://github.com/delos/warm-structure-growth
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