SU(2) CMB & The Cosmological Model
In SU(2), there is a set relationship between the CMB-temperature and redshift (T-z) in adherence to the thermal Sunyaev-Zeldovich effect. Assuming a spatially flat FLRW universe for the cosmological places a modified dark sector connecting ΛCDM between low-z and high-z models into it, and requires a change in the conversion between neutrino temperature and CMB-temperature. With energy conservation, the deconfining phase of SU(2) YM-TD, and a cosmological scale factor a(2.725K) = 1
At high z, the recombination temperature can be modeled as a function of the Thomson scattering rate, while the Hubble parameter depends only on the recombination temperature. Assume that H is matter-dominated during recombination, so that by independence of recombination temperature of the choice of cosmological model, H = Γ. Truly matter-dominated recombination is unphysical, but modeling it gives the redshift relation. The baryonic matter fraction at low-z is small in ΛCDM, positing the emergence of dark matter from a dark-energy like component in the dark sector. A simple model might feature instantaneous release of dark matter from dark energy. A dark sector could be an abundance of non-topological (anti-)vortices in a Planck-scale axion field. The vortices occur as dark energy or dark matter, the expansion of the universe functioning as a conversion between the two. If the dark energy is a homogeneous field contribution of the PSA, which lacks a microscopic model for the ensemble. Emergent components of dark matter complicate the dark sector, though interpolations between smaller, earlier components to the presently observed ones are required by the T-z relation. The mean separation between (anti-)vortex cores in the percolating ensemble is small in cosmological scales, so there are no density contrasts. For a flat, positive interaction potential (within set ranges) with barriers around a critical distance with barriers, which require release of energy from the (anti-)vortices to overcome. This complicates the model unreasonably, and is to be avoided (for now).
The cosmological model can be set up in terms of its Hubble parameter.
The sound horizon r is a high-z variable, given by the Hubble parameter and sound velocity. In ΛCDM, the ratio R can be expressed through entropy density or rescaled energy densities of baryons and photons.
Given the density contrast δ and divergence of fluid velocity θ at conformal time η (differentiation variable) associating with the depercolation redshift, defined as
with α = β = 1, a minimized 𝜒² wrt. Plack power spectra. When the cosmological parameters are fixed through these conditions, α and β can be varied again. The depercolated configurations for Planch-scale axion field have small individual extent on cosmological scales. Vortex loops are non-relativistic particles in isolation with a cosmological equation of at P = 0.
Since only the radiative corrections in SU(2) YM-TD is neglected, and the collisionless Boltzmann equation gives the behavior of co-moving momentum and its modulus q. to define the normal vector. The comoving energy is defined through the scaling function S.
Temperature fluctuations in the V sector can only be propagated via the low-frequency regime in terms of classical electromagnetic waves, which requires an interaction between V and γ. The perturbation theory of this is as follows
The initial conditions are implemented in analogy to those of massive neutrinos.