11.2. The number of Relativistic Particles and their Decays

The main idea here is that the ⁴He abundance depends on the number of relativistic particles during BBN. Extra particles, such as neutrinos or supersymmetric particles, which are relativistic during BBN, lead to faster expansion, larger n/p and a larger Y_p.

Steigman, Schramm & Gunn [169] calculated that BBN limited the number of families to N < 5 to match the ⁴He abundance. The range allowed by SBBN and laboratory measurements have both narrowed over the years and agree well today [170], [11]. A recent update [72] gives N < 3.20 (95%) from SBBN, although a larger range is obtained if a wider variety of measured abundances are accepted [171]. March-Russell et al. [158] note that additional relativistic degrees of freedom are allowed if there is a large compensating asymmetry in the electron neutrino number.

Shi, Fuller & Abazajian [159] follow the time evolution of a lepton number asymmetry arising from active - sterile neutrino transformations during BBN. For _e mixing with _s, Y_p was allowed to change from -1% to +9%, while or _µ mixing with _s allowed -2% to +5%. Hence the Y_p predicted by low D/H in SBBN could be lowered to 0.241, which is between the high and low measurements.

For many years past, observations suggested that Y_p was smaller than expected for the low D/H in the ISM and now QSOs. It is hard to make Y_p lower, since this requires fewer, not more, particles than in SBBN. Holtmann et al. [106], [107] proposed decays of neutrinos, but this is nearly ruled out by the Kamiokande results on atmospheric neutrinos [154].

Lindley [172] found that massive particles decaying into photons must have lifetimes in excess of a few thousand seconds, to avoid the destruction of BBN D. Audouze, Lindley & Silk [173] noted that such radiative decays could photodisintegrate ⁴He and make D and ³He , removing the upper bound on _b . Other references are given by Holtmann et al. [107], who discuss weakly interacting massive (100 GeV) particles which decay of order 10⁶ s after BBN. The authors give limits on the abundance and lifetimes of gravitinos and neutralinos, for a wide range of light nuclei primordial abundances.

Kohri & Yokoyama [174] give limits on the mass fraction in primordial black holes with masses 10⁸ - 3 x 10¹⁰ g which evaporate during BBN and change the abundances.

López-Suárez & Canal [175] combine inhomogeneous nucleosynthesis and particles which decay at a late time to reassess the limits on _b . They find parameters which allow _b < 0.13 - 0.18 h₇₀^-2 (h₇₀^-2 is the Hubble constant in units of 70 km s^-1 Mpc^-1). Such high _b might appear to remove the need for non-baryonic dark matter, but there would then be conflicts with other measures of _b , especially the baryon fraction in clusters of galaxies, if all those baryons were observable today.