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 ∼ 2.725 K (SU(2) CMB ), we investigate how CMB temperature T connects with the cosmological scale factor a in a Friedmann-Lemaître-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between the (instantaneous) redshift of reionisation from CMB observation (z re ∼ 11) and quasar spectra (z re ∼ 6) is repealed. Also, we find that the redshift of CMB decoupling moves from z dec ∼ 1100 to z dec ∼ 1775 which questions 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 eff ∼ 3.36 extracted from Planck data. Interactions between cosmic neutrinos and the CMB implies a common temperature T of (no longer separately conserved) CMB and neutrino fluids. N eff ∼ 3.36 then entails a universal, temperature induced cosmic neutrino mass m ν = ξ T with ξ = 3.973. Our above results on z re and z dec , derived from SU(2) CMB alone, are essentially unaffected when including such a neutrino sector.

SU(2)CMB at high redshifts and the value of H0

“…Conversely, the theoretical prediction of T (z) = g(z)T0 (g the dimensionless function encoded in Fig. 1), being a consequence of SU(2)CMB energy conservation in a FLWR universe Hofmann (2015), immediately implies the according blueshift law ω = g(z)ω0 for the circular frequency of a CMB photon. Since CMB photons in contrast to propagating electromagnetic waves are incoherent fluctuations such a blueshift law has no exploitable information content.…”

“…In Hofmann (2015) the implication of a new SU(2) Yang-Mills theory, describing the CMB as a gas of thermal photons supplemented by a thermal ground state and two invisible vector mode V ± , towards the temperature-redshift (T -z) relation was analysed within an Friedmann-LemaitreRobertson-Walker (FLRW) universe. Due to non-conformal scaling at low z this relation suffers a lower linear slope at high z (z 9) compared to the standard U(1) theory 1 , T T0 = z + 1 , (U(1), ∀z) −→ T T0 = 0.63 (z + 1) , (SU(2) CMB , z 9) ,…”

“…We also skip a discussion of why the critical temperature Tc = T0 (T0 = 2.725 K referring to the present CMB temperature) for the onset of the deconfiningpreconfining phase transition in such a theory is fixed by low-frequency observation of the present CMB, justifying the name SU(2)CMB. To be informed about all this in a pragmatic way we refer the reader to Hofmann (2015), for an in-depth read we propose Hofmann (2016a). We do mention though that the standard relation between neutrino temperature Tν and T , Tν = (4/11) 1/3 T , obtained from entropy conservation during e + e − annihilation, modifies in SU(2)CMB to…”

“…before annihilation) and g1 = 8 (d.o.f. after annihilation), see Hofmann (2015). Note that for, say, z > 100 SU(2)CMB's two massive vector excitations V ± can be considered highly relativistic.…”

“…(1) a slight and inessential correction of the high-z coefficient from 0.62 in Hofmann (2015) to 0.63 is performed which is due to a more precise initial-condition matching for the solution to the energy-conservation equation.…”