Constraining density fluctuations with big bang nucleosynthesis in the era of precision cosmology

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 (∼ 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, η. We find that the deuterium and lithium-7 abundances increase with the RMS fluctuation in η, 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 η to be less than 17% of the mean value of η. This provides us with a new limit on the graininess of the early universe.

Re-evaluation of $Ω_k$ of the normalised Friedmann-Lema\^ıtre-Robertson-Walker model: Implications for Hubble constant determinations

“…Reversal towards the big crunch was avoided because the massive particles were then travelling at relativistic velocities or nearly so, hence H was large. This is consistent with proposals for the mechanism whereby the Universe avoided gravitational collapse [54]. Nevertheless, a short period with Ω rm +Ω m > 1, effecting a considerable drag on particle velocity, is consistent with a H at recombination not too different than H 0 .…”

Stellar signatures of inhomogeneous big bang nucleosynthesis

“…However, such patches are rare for two reasons: first, standard BBN is a great success, and limits on inhomogeneity on horizon patches are ≲17%, expressed in terms of Δη [21]. Second, the Universe in the BBN epoch is highly radiation dominated, and the associated PBHs must be subdominant by a factor of at least ð1 þ z BBN Þ=ð1 þ z eq Þ ∼ 10 4 [22].…”

Random Spherical Hyperbolic Diffusion

“…Some basic considerations on diffusion length are given in Appendix A. After allowing for neutron back-diffusion to proton-rich regions where neutrons have been further depleted by fusion [34], the observed distribution of elements and temperature variations constrains the parameters of heterogeneous models [7], [21].…”