Probing the small-scale primordial power spectrum via relic neutrinos and acoustic reheating

Abstract

We show that the dissipation of small-scale perturbations through diffusion damping after neutrino decoupling lowers the present-day neutrino temperature compared to the expected value of $1.96\text{K}$. This reduces the relic neutrino abundance by an amount controlled by the integral of the primordial curvature power spectrum ${\Delta }_{\mathcal{R}}^2(k)$. We find that a relic neutrino detection by PTOLEMY can set limits ${\Delta }_{\mathcal{R}}^2(k)\lesssim \mathcal{O}(0.1)$ on scales $k\lesssim 3\times 10^5{\text{Mpc}}^{-1}$, complementary to limits from Big Bang Nucleosynthesis, spectral distortions, pulsar timing arrays, and future dark ages 21-cm observations.

Comments: 7 pages, 3 sub-figures arranged into 2 figures