Relic photon temperature versus redshift and the cosmic neutrino background

Abstract: Presuming that CMB photons are described by the deconfining phase of an SU(2) Yang-Mills theory with the critical temperature for the deconfining-preconfining phase transition matching the present CMB temperature $T_0\sim 2.725\,$K (SU(2)${\tiny{CMB}}$), we investigate how CMB temperature $T$ connects with the cosmological scale factor $a$ in a Friedmann-Lema^itre-Robertson-Walker Universe. Owing to a violation of conformal scaling at late times, the tension between the (instantaneous) redshift of reionisation from CMB observation ($z{\tiny{re}}\sim 11$) and quasar spectra ($z_{\tiny{re}}\sim 6$) is repealed. Also, we find that the redshift of CMB decoupling moves from $z_{\tiny{dec}}\sim 1100$ to $z_{\tiny{dec}}\sim 1775$ which questions $\Lambda$CDM cosmology at high redshifts. Adapting this model to the conventional physics of three flavours of massless cosmic neutrinos, we demonstrate inconsistency with the value N${\tiny{eff}}\sim 3.36$ extracted from Planck data. Interactions between cosmic neutrinos and the CMB implies a {\sl common} temperature $T$ of (no longer separately conserved) CMB and neutrino fluids. N${\tiny{eff}}\sim 3.36$ then entails a universal, temperature induced cosmic neutrino mass $m_\nu=\xi T$ with $\xi=3.973$. Our above results on $z_{\tiny{re}}$ and $z_{\tiny{dec}}$, derived from SU(2)$_{\tiny{CMB}}$ alone, are essentially unaffected when including such a neutrino sector.