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

TL;DR

This paper demonstrates how small-scale primordial perturbations affect relic neutrino temperatures and abundance, proposing that neutrino detection can constrain primordial power spectrum at very small scales.

Contribution

It introduces a novel method to probe small-scale primordial fluctuations through relic neutrino measurements, complementing existing cosmological constraints.

Findings

Relic neutrino temperature is lowered due to diffusion damping of small-scale perturbations.

Detection of relic neutrinos can constrain the primordial curvature power spectrum at scales up to 3×10^5 Mpc^{-1}.

Limits from neutrino observations are complementary to those from BBN, spectral distortions, pulsar timing, and 21-cm observations.

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 $\Delta_{\cal R}^2(k)$. We find that a relic neutrino detection by PTOLEMY can set limits $\Delta_{\cal R}^2(k) \lesssim {\cal O}(0.1)$ 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.