6 research outputs found
Big Bang Nucleosynthesis with Gaussian Inhomogeneous Neutrino Degeneracy
We consider the effect of inhomogeneous neutrino degeneracy on Big Bang
nucleosynthesis for the case where the distribution of neutrino chemical
potentials is given by a Gaussian. The chemical potential fluctuations are
taken to be isocurvature, so that only inhomogeneities in the electron chemical
potential are relevant. Then the final element abundances are a function only
of the baryon-photon ratio , the effective number of additional neutrinos
, the mean electron neutrino degeneracy parameter , and
the rms fluctuation of the degeneracy parameter, . We find that for
fixed , , and , the abundances of helium-4,
deuterium, and lithium-7 are, in general, increasing functions of .
Hence, the effect of adding a Gaussian distribution for the electron neutrino
degeneracy parameter is to decrease the allowed range for . We show that
this result can be generalized to a wide variety of distributions for .Comment: 9 pages, 3 figures, added discussion of neutrino oscillations,
altered presentation of figure
Inhomogeneous Neutrino Degeneracy and Big Bang Nucleosynthesis
We examine Big Bang nucleosynthesis (BBN) in the case of inhomogenous
neutrino degeneracy, in the limit where the fluctuations are sufficiently small
on large length scales that the present-day element abundances are homogeneous.
We consider two representive cases: degeneracy of the electron neutrino alone,
and equal chemical potentials for all three neutrinos. We use a linear
programming method to constrain an arbitrary distribution of the chemical
potentials. For the current set of (highly-restrictive) limits on the
primordial element abundances, homogeneous neutrino degeneracy barely changes
the allowed range of the baryon-to-photon ratio. Inhomogeneous degeneracy
allows for little change in the lower bound on the baryon-to-photon ratio, but
the upper bound in this case can be as large as 1.1 \times 10^{-8} (only
electron neutrino degeneracy) or 1.0 \times 10^{-9} (equal degeneracies for all
three neutrinos). For the case of inhomogeneous neutrino degeneracy, we show
that there is no BBN upper bound on the neutrino energy density, which is
bounded in this case only by limits from structure formation and the cosmic
microwave background.Comment: 6 pages, no figure