Advances in High Energy Physics

Volume 2017, Article ID 7525121, 9 pages

https://doi.org/10.1155/2017/7525121

## Cosmic Microwave Background as a Thermal Gas of SU(2) Photons: Implications for the High- Cosmological Model and the Value of

^{1}Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany^{2}Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

Correspondence should be addressed to Steffen Hahn; moc.liamg@nhah.t.neffets

Received 9 May 2017; Revised 20 June 2017; Accepted 16 July 2017; Published 16 October 2017

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2017 Steffen Hahn and Ralf Hofmann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

Presently, we are facing a tension in the most basic cosmological parameter, the Hubble constant . This tension arises when fitting the Lambda-cold-dark-matter model (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() rather than U() gauge principle, suggesting a high- 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-) extraction of the relation between the comoving sound horizon at the end of the baryon drag epoch and (). 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 tension actually transforms into a discrepancy. To make contact with successful low- 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- model we compute the angular scale of the sound horizon at photon decoupling.

#### 1. Introduction

Since the pioneering work by Yang and Mills [1] on the definition of a local four-dimensional, classical, and minimal field theory, which is based on the nonabelian gauge group SU(), much progress has been made in elucidating the role of topologically stabilized and (anti)-self-dual field configurations in building the nonperturbative ground state and influencing the properties of its excitations [2–8]. In particular, the deconfining phase is subject to a highly accurate thermal ground state estimate [9, 10], being composed of so-called Harrington-Shepard (anti)calorons [11]. This (cosmologically relevant) ground state invokes both an adjoint Higgs mechanism [12–15], rendering two out of three directions of the SU() algebra massive (free thermal quasiparticles), and a chiral anomaly [2, 3, 5, 6], giving mass to the Goldstone mode induced by the associated dynamical breaking of this global symmetry. Radiative corrections to thermodynamical quantities, evaluated on the level of free thermal (quasi)particles, are minute and well under control [9, 10]. Note that this is in contrast to the large effects of radiative corrections attributed to the effective QCD action at zero temperature in [16, 17] which are exploited as potential inducers of vacuum energy in the cosmological context in [18–22]. However, it was argued in [23, 24] that QCD condensates, which contribute to the trace anomaly of the energy-momentum tensor (as implied by the effective action), do not act cosmologically.

Postulating that thermal photon gases obey an SU() rather than a U() gauge principle, the SU() Yang-Mills scale can be inferred from low-(radio)frequency spectral intensity measurements, for example [25], of the Cosmic Microwave Background (CMB) [26], prompting the name . Below we will use the name synonymously for the implied cosmological model. To investigate the consequences of this postulate towards the equation of state radiative corrections are entirely negligible [9]. When subjecting local energy conservation in a Friedmann-Lemaître-Robertson-Walker (FLRW) universe to this equation of state the numerical temperature ()-redshift () relation () of the CMB follows; see Figure 1 [27, 28], where a comparison with the conventional U() photon gas is shown. The curvature of ( K denoting today’s CMB temperature) at low is due to the influence of the SU() Yang-Mills mass scale on the equation of state. In [28] an argument is given why recent observational “extractions” of , which claim no deviations from the conventional behavior , are circular. One has at high and therefore a lower slope compared to the conventional case. In an approximation, where recombination at is subjected to thermodynamics, the decoupling condition is where denotes the Thomson photon-electron scattering rate at the decoupling temperature K. We have where and denote the respective ratios of today’s energy densities in baryons and cold dark matter to the critical density. Since this roughly matches . If a strong matter domination can be assumed during recombination then should be equal to but, due to matter-radiation equality occurring at in , this assumption is not quite met, explaining the mild discrepancy between and . Still, we take this rough argument and the desired minimality of the cosmological model as motivations to omit cold dark matter in the high- cosmological model which operates down to recombination and well beyond it.