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

Abstract

Inhomogeneous big bang nucleosynthesis (BBN) produces a spatially inhomogeneous distribution of element abundances at T ∼ 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 dcom ≈ 70 pc for all of the elements of interest except 7 Li, for which dcom 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.Since its development in the 1960s [1-4] big bang nucleosynthesis (BBN) has become one of the main pillars of modern cosmology. While the baryon-photon ratio, η, was once treated as the main quantity to be determined by comparing the predictions of BBN to the observed element abundances, the independent measurement of η from CMB observations has left the theory of BBN with no free parameters. Given the allowed range for η derived from the CMB, the predicted BBN abundances of deuterium and 4 He are in excellent agreement with the observations. However, the predicted 7 Li abundance remains a factor of three larger than the abundance inferred from observations; this discrepancy remains unexplained at present [5]. For a recent review of BBN, see Ref. [6].Despite the successes of BBN, many modifications to the theory have been proposed. Perhaps the most widely investigated of these modified theories are models involving some sort of inhomogeneity at the epoch of BBN. The most basic of such models postulate isocurvature fluctuations, for which η varies from one region of the Universe to another [7][8][9][10][11][12][13]. Most of these investigations simply calculate the element abundances as a function of η in separate domains and average the final results. However, an important effect arises when the length scale of the fluctuations is longer than the proton diffusion length but shorter than the neutron diffusion length; in this case neutron diffusion from high-density to low-density regions will strongly modify the neutron-proton ratio. These models were initially inspired by the possibility of such density fluctuations arising naturally in the QCD phase transition [14,15], and this line of investigation yielded an extensive literature (see, e.g., Ref.[16] and references therein). Furthermore, several authors have pointed out that small regions with very large values of η could lead to the primordial production of elements much heavier ...