11.1. Inhomogeneous BBN

Following early discussion of inhomogeneous BBN (IBBN) by Epstein & Lattimer [163] and Hogan [164], many detailed studies of different types of inhomoegeneity have been published.�� Malaney & Mathews [165] and Kainulainen, Kurki-Suonio, & Sihvola [154] give reviews.

IBBN has been discussed to allow larger _b than standard BBN, to allow differing values of D/H in the universe, and to reconcile low Y_p with low D/H values.

One exciting goal of this work was to determine whether inhomogeneity could give the observed abundances with _b much larger than the usual value, and perhaps large enough to account for all gravitating matter, without the need for non-baryonic dark matter (e.g. [164], [104], [108]). The best upper limit on _b comes from the lowest observed D/H, which until recently was in the ISM. In standard BBN, a higher _b is ruled out because BBN would make less than the observed ISM D/H, and no other way to make D is known. In IBBN the D/H in the ISM comes from low density regions, allowing a higher average density. The current observations, with some exceptions, fit SBBN well, and hence IBBN allows only a slight increase in _b.

Inhomogenieties can be imagined over a wide range of distance scales. The smallest scales, < 10^-5 pc, mix prior to BBN, leaving homogeneous SBBN. Small scales mix during BBN. Intermediate scales which mix after BBN give abundances which are constant in space today, but the abundances are different from SBBN with the same _b. Extra D would be made in regions with low density during BBN, giving enhanced D/H everywhere today. Large scales (> 1 kpc) may have avoided mixing, and could give different D/H in different locations today. The near isotropy of the CMB limits inhomogenieties to < 1 Mpc.

Jedamzik & Fuller [47] found it difficult to match observed abundances of ⁷Li with large scale primordial isocurvature baryon number fluctuations. Most overly dense regions of the universe with masses greater than the local baryon Jeans mass would have to collapse (to prevent observation of the ⁷Li which is overproduced) and smaller scale fluctuations would have to be absent or suppressed. Gnedin, Ostriker & Rees [166] and Copi, Olive & Schramm [167] reached similar conclusions. Copi, Olive & Schramm [168] also showed that large scale (>> 1 Mpc) isocurvature perturbations conflict with the smoothness of the CMB, but do not rule out inhomogeneity [52]. _b Kainulainen, Kurki-Suonio, & Sihvola [154] review IBBN. The _b can be higher than in SBBN provided the distance scale of the baryon inhomogeneity is near to optimal to maximize neutron diffusion effects. The distance scale expected for inhomogeneities arising in the electroweak transition are too small (10^-6 to 10^-3 pc today) to have major effects, although not below the accuracy of BBN abundance calculations. QCD inhomogeneities are not so limited. However, a low D/H < 5 x 10^-5 still requires Y_p > 0.240 even in IBBN, which helps reconcile low D/H and low Y_p measurements, especially when we accept that the errors on Y_p are larger than quoted. _b Rehm & Jedamzik [161] studied BBN in the presence of anti-matter domains. Annihilation is preferentially on neutrons, and in a limiting case the resulting universe is without light nuclei, in violation of the measured abundances. With small amount of anti-matter, both the low Y_p and low D/H measurements are matched.

Early IBBN results looked promising. Today it appears that the scales are too small to have major effects, and measurements of primordial abundances, especially upper limits on ⁷Li , with modest depletion (< factor of two), are usually used to give limits on the inhomogeneity, rather than to argue that inhomogeneity helps explain discordant data or allows different conclusions about _b.