Cosmic Microwave Background as a thermal gas of SU(2) photons: Implications for the high-z cosmological model and the value of $H_0$

Abstract

Presently, we are facing a 3$σ$ tension in the most basic cosmological parameter -- the Hubble constant $H_0$. This tension arises when fitting the Lambda-cold-dark-matter model ($Λ$CDM) to the high-precision temperature-temperature (TT) power spectrum of the Cosmic Microwave Background (CMB) and to local cosmological observations. We propose a resolution of this problem by postulating that the thermal photon gas of the CMB obeys an SU(2) rather than U(1) gauge principle, suggesting a high-$z$ cosmological model which is void of dark matter. Observationally, we rely on precise low-frequency intensity measurements in the CMB spectrum and on a recent model independent (low-$z$) extraction of the relation between the comoving sound horizon $r_s$ at the end of the baryon drag epoch and $H_0$ ($r_s H_0 = \text{const}$). We point out that the commonly employed condition for baryon-velocity freeze-out is imprecise, judged by a careful inspection of the formal solution to the associated Euler equation. As a consequence, the above mentioned 3$σ$ tension actually transforms into a 5$σ$ discrepancy. To make contact with successful low-$z$ $Λ$CDM cosmology we propose an interpolation based on percolated/depercolated vortices of a Planck-scale axion condensate. For a first consistency test of such an all-$z$ model we compute the angular scale of the sound horizon at photon decoupling.