Scale Invariant CMB Analysis

Mathematical analysis and the architecture of the Cosmic Microwave Background (CMB) show that it is a realistic fractal, remarkably close to being scale invariant, a property that is a defining feature of self similar shapes or fractional dimensional curves. The near perfect scale invariance of the CMB's primordial fluctuations provides one of the strongest pieces of evidence for the theory of cosmic inflation. This inflation is deeply rooted in general relativity and quantum mechanics, with the Yang-Mills matrix scale invariance reflected in the inflationary model.

The tiny fluctuations of temperature of the CMB are believed to be the progenitors of all large scale cosmic structures, from nebulae to galaxies and the clusters of them. Inflationary theory proposes that exponential expansion, or perhaps fractal, generated from quantum mechanics (although spontaneous symmetry breaking is an issue) is isomorphic or mapped to the fluctuations of the early universe.

A "flat" power spectrum from the inflationary theory, supported by COBE, WMAP, and Planck, suggest a perfectly scale invariant amplitude at all spatial scales of the photons generated from expansion. In quantum, the power spectrum comes from the raising and lowering operators and second quantization. These values generate the Hamiltonian, Poynting vector, and energy density term useful in relativity.

There is a slight deviation or red shift from a perfect scale invariant system. This means that the large scale system is slightly more random (perhaps a Riemann zeta function distribution is nested in here) than the small scale.

Fractal like properties and the non-Gaussian debate indicate that the overall power spectrum confirms near scale invariance in the fractal CMB map. Isothermal line analysis (showing the zeta), non-Gaussianity, and a new Standard Model will show CMB fractal characteristics.

General Physics scientists utilize the map of the grand universe to get an idea of the shape of phenomena and their first order expansions here on Earth. A good approximation of things with the CMB fractal distribution indicates the direction of higher order Taylor series functions for analysis in fields from thermodynamics and plasma physics to economics.