CMB Statistical Isotropy Breaking
Dynamical breaking of statistical isotropy at late times in universe history, arises if modeled through SU(2) electromagnetic field gauge group. The local SU(2)-induced depression in CMB temperature against the forward lightcone influences the statistics and angular correlation of primordial temperature fluctuations. The cosmic standard model includes gravitational instabilities through statistically homogeneous primordial matter-density fluctuations. The CMB photons should stream freely toward the observer, safe for tiny plasma imprints. In the observations, the radiance within a small frequency band is converted to temperature using the Planck BBR-law. Above 20 GHz, this is unproblematic, but in the deep Rayleigh-Jeans regime (below 3 GHz), the temperature drops without sufficient explanation.
The frequency bands and angular regions for the measurements determine the degree of observed temperature anisotropy, and its sensitivity to noise. Statistical errors can be minimized by multiple passes. The CMB map can be decomposed into a basis of spherical harmonics and statistical isotropy, normalized sums over the m = -/+l over the squares of the expansion coefficients in the temperature-temperature correlation function's multipole power. The CSM spectrum turns out near scale-invariant.
Some observations implying violations of statistical isotropy:
Large angle suppression of the correlation function - the product of temperature in 2 pixels separated by the angle parameter, averaged over pixel pairs - sees an unexpected decrease at angles over 60 degrees, and the entire northern ecliptic hemisphere.
A nonzero variance of temperature fluctuations between the northern map hemisphere and the southern one.
A plane close to the ecliptic sees a difference between the average amplitudes of temperature fluctuations in either half.
The famous cold spot of the CMB map is not at all centered.
The CMB quadrupole with the octupole is highly improbable, but turns out at about 9 degrees.
The reflected temperature fluctuations are misaligned by about 42 degrees.
They don't really effect the fits for cosmological parameters, so their hypothesis of a flat, accelerating universe originating from a nearly statistically homogenous Gaussian density-perturbation is also unaffected. The larger discrepancy can be found in the Hubble parameter determined through the CMB and the astronomical data. These observations can be modeled through a multiplicative, dipolar modulation along some direction vector p.
where n is a statistical noise field, s is a hypothetical isotropic CMB sky, and A the modulation amplitude. Using the bipolar spherical harmonic formalism (bipolar spherical harmonic formalism) by generalizing the angular power spectrum in allowing cross correlations between m, l, the statistical isotropy can be modeled more subtly. This also works for A, p, without change of significance for these parameters at higher angular resolutions. It follows that the dipolar modulation is attributed to low values of l, so to a local origin of large-angle anomalies. Interpreting p as a local gradient to a statistically isotropic field, coupling to the CMB makes the modulation physical. If the statistical isotropy of the CMB is broken, then there is no reason to further assume a U(1) gauge group for the collective description of Cooper-pair condensates. Instead, SU(2) is better suited, because the (anti)-caloron pair construction contains massive vector modes that give rise to tightly controlled radiative corrections, observable in the thermal propagation of some third, massless photon species at low temperatures and frequencies. The m-number diverges when approaching critical temperature, so no radiative corrections can take place for thermal photons, meaning that they should adhere exactly to the Planck radiation law. The thermal ground state of the preconfining phase consists of massless monopoles, exposing the photon to a superconductivity-esque Meissner effect. The SU(2) gauge theory exhibits asymptotic freedom, characterized by 2 immediate properties, so low-temperature observables are independent of initial conditions in high temperature, and the an intrinsic mass scale, parametrizing the temperature dependence of m.