Thermal photon number density is proportional to . A sudden photon heating factor therefore raises photon number by and dilutes the baryon-to-photon ratio by its inverse when baryon number is conserved. Comparing Big Bang nucleosynthesis and Cosmic microwave background baryon-density determinations can test entropy injection between the two epochs, subject to changes in the expansion rate and nuclear abundances.
Cosmological lepton asymmetry 2026-09-28
Helium-4 Created 2026-10-06 Updated 2026-10-07
Helium-4 is the stable helium isotope with two protons and two neutrons; its nucleus is an alpha particle. Its strong binding makes it the principal neutron-containing product of primordial Big Bang nucleosynthesis.
Past exam of the mathematics course of the University of Cambridge 2010 ii Paper 3 15D Solution Created 2026-09-24 Updated 2026-09-24
Past exam of the mathematics course of the University of Cambridge 2012 iii Paper 53 2 Created 2026-10-03 Updated 2026-10-07
For a quantitative thermal-relic prediction, assume one ordinary weakly interacting neutrino flavor: one populated neutrino helicity and one antineutrino helicity, negligible chemical potential, early thermal equilibrium, and relativistic decoupling around the MeV epoch. Equal neutrino and antineutrino populations imply no new lepton asymmetry. The Fermi-Dirac distribution is maintained while the weak interaction rate exceeds the expansion rate. After neutrino decoupling, the distribution free streams, its momentum scale falls as , and its comoving number is conserved. A mass of is negligible at Big Bang nucleosynthesis temperatures, but the relic later becomes nonrelativistic. Its energy density then changes from radiation-like scaling to matter-like scaling. Stability prevents its removal by decay; decoupling while relativistic prevents a subsequent equilibrium Boltzmann suppression of its number.