Revisiting constraints on small scale perturbations from big-bang nucleosynthesis

TL;DR

This paper refines constraints on small-scale density perturbations from big-bang nucleosynthesis by accounting for local temperature variations, resulting in a tighter limit on the curvature perturbation spectrum.

Contribution

It provides a detailed calculation of neutron-proton freeze-out considering local temperature patches, improving previous constraints on small-scale perturbations.

Findings

Small scale perturbations decrease the neutron-proton ratio.

Constraint on curvature perturbations: $ riangle^2_ ext{R} ot o 0.018$ for $10^4$ to $10^5$ Mpc$^{-1}$.

Refined analysis alters previous understanding of perturbation effects.

Abstract

We revisit the constraints on the small scale density perturbations ($10^4\,\mathrm{Mpc}^{-1}\lesssim k \lesssim10^5\,\mathrm{Mpc}^{-1}$) from the modification of the freeze-out value of the neutron-proton ratio at big-bang nucleosynthesis era. Around the freeze-out temperature $T\sim 0.5\,\mathrm{MeV}$, the universe can be divided into several local patches which have different temperatures since any perturbation which enters the horizon after the neutrino decoupling has not diffused yet. Taking account of this situation, we calculate the freeze-out value in detail. We find that the small scale perturbations decrease the n-p ratio in contrast to previous works. With use of the latest observed $^4$He abundance, we obtain the constraint on the power spectrum of the curvature perturbations as $\Delta^2_\mathcal{R}\lesssim 0.018$ on $10^4\,\mathrm{Mpc}^{-1}\lesssim k \lesssim 10^5\,\mathrm{Mpc}^{-1}$.