Neutrino Decoupling When Post-Bounce Reheating Ends Late: Incomplete Thermalisation and the Radiation Density

Standard cosmology assumes reheating finished long before neutrinos decoupled, so neutrinos enter the MeV era with a full equilibrium abundance. A bounce history with very late reheating breaks that assumption. This study computes, for reheating completion temperatures from 1 to 40 MeV, what fraction of the equilibrium neutrino abundance is actually established and what effective radiation density results. Completion below about 2 MeV leaves a large deficit, and by about 5 MeV the standard value is recovered; the calculation quantifies the transition rather than assuming the standard value. The study is computed from stated assumptions and is not a measurement. If reheating completes at 1 MeV, the neutrino interaction rate at completion is 3.05e-01 times the expansion rate, neutrinos reach a fraction 0.263 of full equilibrium abundance, and the effective number of relativistic species is 0.801 rather than the standard 3.046. If reheating completes at 2 MeV, the neutrino interaction rate at completion is 2.44e+00 times the expansion rate, neutrinos reach a fraction 0.913 of full equilibrium abundance, and the effective number of relativistic species is 2.781 rather than the standard 3.046.