Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies

¹ Institut für Theoretische Physik Universität Heidelberg Philosophenweg 16 69120 Heidelberg, Germany
² Institut für Photonenforschung und Synchrotronstrahlung Karlsruher Institut für Technologie Hermann-von-Helmholtz Platz 1 Eggenstein-Leopoldshafen, Germany

^a e-mail: r.hofmann@thphys.uni-heidelberg.de

Published online: 29 April 2014

Abstract

A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (anti)selfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anti)calorons of scale parameter ρ ∼ |φ|⁻¹ contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anti)caloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anti)caloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in confining phases of SU(2) Yang-Mills theories neutrino mass m_ν solely arises by interactions with an environment. Cosmologically, the CMB represents this environment, and thus one would expect that m_ν = ξT where ξ = O(1). In this model cosmic neutrinos are a small dark-matter contribution, conserved only together with the CMB fluid, influencing Baryonic Acoustic Oscillations during CMB decoupling.