Does inhomogeneous big bang nucleosynthesis produce an inhomogeneous element distribution today?

TL;DR

This paper investigates whether inhomogeneities from big bang nucleosynthesis could still cause uneven element distributions today, finding that large-scale inhomogeneities might persist while smaller ones are smoothed out.

Contribution

It calculates the cosmological diffusion length of BBN elements and assesses their impact on present-day element distribution heterogeneity.

Findings

Diffusion length for most elements is about 70 parsecs today.

$^7$Li remains ionized longer, resulting in a smaller diffusion length.

Large-scale inhomogeneities could survive to the present day.

Abstract

Inhomogeneous big bang nucleosynthesis (BBN) produces a spatially inhomogeneous distribution of element abundances at $T \sim 10^9$ K, but subsequent element diffusion will tend to erase these inhomogeneities. We calculate the cosmological comoving diffusion length for the BBN elements. This diffusion length is limited by atomic scattering and is therefore dominated by diffusion when the atoms are neutral, between the redshifts of recombination and reionization. We find that the comoving diffusion length today is $d_{com} \approx 70$ pc for all of the elements of interest except $^7$Li, for which $d_{com}$ is an order of magnitude smaller because $^7$Li remains ionized throughout the relevant epoch. This comoving diffusion length corresponds to a substellar baryonic mass scale and is roughly equal to the horizon scale at BBN. These results lend support to the possibility that inhomogeneities on scales larger than the horizon at BBN could lead to a spatially inhomogeneous distribution of elements today, while purely subhorizon fluctuations at BBN can result only in a homogeneous element distribution at present.