YM-Thermodynamics 2024, 44: CMB & Determination of Critical Temperature
In the CMB, photon propagation is fundamentally ruled by an SU(2) rather an a U(1) gauge. In a thermal pure and deconfining SU(2) gauge theory, the SU(2) to U(1) symmetry breaking is induced by the effective thermal ground-state estimate. Fundamental SU(2) YM-theory emerges from spatial coarse-graining over interacting calorons of topological charge modulus one. Below critical temperature, the photon mass is generated by the Meissner effect arising from a condensate of monopoles, influencing the CMB at very low frequencies.
The spectral energy density I(ω) of a gas of free (transverse) photons in thermal equilibrium with a heat reservoir is given by the number of modes per volume, available in some frequency interval times the average thermal energy per mode.
The value of the critical temperature at around 2.73 K is based on several pieces of evidence:
The magnitude of extragalactic magnetic fields, can be bounded from above via measurements of Faraday rotation in the polarized radio emission from distant quasars and/or distortions of the spectrum and polarization properties of the CMB. This gives upper limits for the primordial field strengths, significantly below galactic fields. Primordial seed fields are hence assumed to be amplified. This leaves the magnetohydrodynamics unchecked. A sensible lower bound can be found at about the critical temperature.
A gradual metamorphosis of cold extended objects, observed with a brightness temperature of about 20 K with cold regions of 5 - 10 K and an atomic number density of about 1.5 per cubic centimeter. The 2-point correlator of photonic energy density at these temperatures, assuming a critical temperature of 2.725 K, the correlator gets suppressed by up to a factor of two at the typical interatomic distances. The resulting Coulomb potential is given as
Suppression of Coulomb potential should have an analogue in the dipole-dipole interaction responsible for the formation of hydrogen molecules for hydrogen atoms in the standard theory. This can only be relevant to cold temperatures.
Just slightly below CMB baseline temperature, an excess of CMB intensity can be observed at low frequencies with physics of the deconfining-preconfining phase-transition under which the photon acquires a Meissner mass by its direct coupling to the superconducting thermal ground state inside the preconfining phase. The tree-level massless mode, acquires a Meissner mass. The dual gauge coupling vanishes at critical temperatures, then rises rapidly as temperature decreases, before vanishing again in the deconfining phase. The energy leaves the photon sector to reappear in terms of (anti)monopole mass in the deconfining phase, and no evanescent photon fields are generated at low frequencies. At critical temperature, no spectral are thermodynamically decoupled. The preconfining side photons don't propagate. The spectral intensity attributed to a transient photon field with random fluctuations in phase and amplitude are not thermalized. Its photons carry the energy density lost by formerly massless photons.
CMB temperatures below critical introduces tiny coupling to the SU(2) preconfining ground state, endowing low-frequency photons with a Meissner mass after propagating for sufficient time above ground state. A calibrator photon, is fresh in that the distance between emission at the black-body wall and absorption is just a small multiple of its wavelength. At sufficiently small coupling, this propagation path is insufficient to generate the Meissner mass even at low frequencies.
