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 Yp 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
Yp > 0.240
even in IBBN, which helps reconcile low D/H and low Yp
measurements,
especially when we accept that the errors on Yp 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
Yp 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.