The Neutrino Paradox: Mathematical Inconsistency of Hot Big Bang Thermodynamics A Falsification Test for the Standard Cosmological Model
Abstract:
The standard Hot Big Bang (HBB) model predicts thermal production of relic neutrinos with number density n_ν ≈ 336 cm⁻³ at decoupling temperature T_dec ≈ 1 MeV. If neutrino energy does not undergo “cooling” (via metric redshift or other mechanism), the current mean energy would be ⟨E_ν⟨ ≈ 3.8 MeV, yielding energy density ρ_ν ≈ 1.3×10⁹ eV·cm⁻³, approximately 2.5×10⁵ times larger than the measured critical density ρ_crit ≈ 5×10³ eV·cm⁻³. This pure mathematical inconsistency requires either abandonment of thermal HBB, or acceptance of universal metric redshift E ⟨ 1/a. Neutrino observations from supernova SN1987A (z_cosmological ≈ 10⁻⁵) cannot discriminate redshift at this level but provide upper limits (z_ν < 10⁻⁴). We propose a multi-method experimental program to test redshift universality: (1) re-analyzed SN1987A data, (2) future supernovae at z > 0.01, (3) Diffuse Supernova Neutrino Background (DSNB), (4) direct Cosmic Neutrino Background (CνB) detection via tritium capture. A “golden event” (core-collapse supernova at z > 0.01 with >500 detected neutrinos) expected in 2027-2035 will provide definitive discrimination: if |z_ν - z_γ| > 3σ, ΛCDM is falsified and alternative frameworks (NMSI) become necessary.
