Constraining Density Fluctuations with Big Bang Nucleosynthesis in the Era of Precision Cosmology

TL;DR

This paper investigates how large-scale baryon density inhomogeneities affect primordial element abundances during Big Bang Nucleosynthesis, deriving constraints on early universe density fluctuations from observed deuterium levels.

Contribution

It introduces a method to analyze inhomogeneous BBN with fluctuations larger than neutron diffusion length, providing new limits on early universe density variations.

Findings

Deuterium and lithium-7 abundances increase with RMS fluctuation in baryon/photon ratio.

Helium-4 abundance is less affected by density fluctuations.

Observational data constrains RMS fluctuation in η to less than 17%.

Abstract

We reexamine big bang nucleosynthesis with large-scale baryon density inhomogeneities when the length scale of the density fluctuations exceeds the neutron diffusion length ($\sim 10^7-10^8$ cm at BBN), and the amplitude of the fluctuations is sufficiently small to prevent gravitational collapse. In this limit, the final light element abundances can be determined by simply mixing the abundances from regions with different baryon/photon ratios without interactions. We examine gaussian, lognormal, and gamma distributions for the baryon/photon ratio, $\eta $. We find that the deuterium and lithium-7 abundances increase with the RMS fluctuation in $\eta $, while the effect on helium-4 is much smaller. We show that these increases in the deuterium and lithium-7 abundances are a consequence of Jensen's inequality, and we derive analytic approximations for these abundances in the limit of small RMS fluctuations. Observational upper limits on the primordial deuterium abundance constrain the RMS fluctuation in $\eta $ to be less than $17\%$ of the mean value of $\eta $. This provides us with a new limit on the graininess of the early universe.