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 ($\sim 10^7-10^8$ 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.

8 pages, 2 figures, reaction rates updated, minor changes to figures and limits, added analytic approximations for element abundances and discussion of Jensen's inequality, to appear in Phys. Rev. D

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• BBN constraints on dark radiation isocurvature
• Effects of anisotropy in an anisotropic extension of $w$CDM model
• Constraints on running vacuum models with the baryon-to-photon ratio
• Re-evaluation of ${\Omega }_k$ of the normalised Friedmann-Lema\^ıtre-Robertson-Walker model: Implications for Hubble constant determinations
• Does inhomogeneous big bang nucleosynthesis produce an inhomogeneous element distribution today?
• Decay of baryon inhomogeneities in an expanding universe