Dark Matter Update

Let us recall the basic dark matter fractions in the quark gluon plasma. That's $3 / 4 \pi$ for the dark matter fraction and $9/ 4 \pi$ for the (so called) dark energy, with the baryonic fraction $\Omega_{b} = 1 - 3/ \pi$, as confirmed by WMAP.

In the information theory, we need two kinds of dimension. First, path bases define an integral dimension, $27$ for the Jordan algebra. But complex matrix entries tend to be characters for finite fields, so that the root of unity corresponding to a phase $2 \pi /27$ would specify the cardinality of a field with $27$ elements. These two dimension types should be related by the mirror physics that explains the dark matter fractions.

A dark matter ansatz: the total dark sector density fraction $\Omega_{d}$, as a fraction of the character dimension for $27$ paths, equals the observable universal fraction of the integral dimension. In other words, we would like to write

$ \frac{3}{\pi} \frac{2 \pi}{27} = \frac{2}{9} $

so that $\Omega_{d} = 3/ \pi$. Now observe that we can split the dark sector into quark and lepton components. The leptonic dark matter fraction $3/ 4 \pi$ now corresponds to the fraction $1/18$, a single quark path from the quark set. Similarly, the dark energy fraction $9/ 4 \pi$ corresponds to the fraction $1/6$, a single lepton path. The total $3/ \pi$ is then the only solution obeying this quark lepton complementarity.

In the quark gluon plasma, the minimal viscosity to entropy ratio is $1/ 4 \pi$. As a character dimension fraction, $1/ 4 \pi$ corresponds to $1/54$, a single basis path in the full bioctonion algebra.