WMAP Update

Wondrous Kea has suggested comparing predictions of $\Omega_b$ and $\Omega_m$ with the latest WMAP results. Data comes from Spergel et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations

Our 4-dimensional spherical Space has a finite volume given by:

V = 2 $\pi$^2 R^3

Where R is radius, with dimensions of length. The very gravity which causes Space/Time to be curved would cause the sphere to collapse, unless it were already expanding. We can express the expanding Universe simply:

R = ct

Again R has dimensions of length and c has dimensions of distance/time. For an expanding Universe, it is axiomatic that R is some multiple of t.

The Universe can't expand at the same rate c forever, for gravity slows it down. We do some math and get:

GM = tc^3

Where GM combines mass of the Universe with its gravitational constant.

Together these simple expressions form a solution to the Einstein-Friedmann equations with stable density:

$\rho$f = (6 $\pi$ G t^2)^{-1}

Here we encounter an interesting difference. If an initial mass M is distributed among this spherical volume V, we get an initial density $\rho$i of:

$\rho$i = M/V where M = (tc^3)/G

$\rho$i = (2 $\pi$G t^2)^{-1}

The difference is made up by the matter we are made of. When the Universe is "underweight," quantum mechanics predicts that matter will appear via pair production. The amount of this matter is the difference between $\rho$i and $\rho$f, or 4.507034%.

Prediction: 4.507034%

$\Omega_b$ 4.49 ± 0.28 (Prediction correct within 0.6 standard deviations)

$\Omega_m$ is the amount of "dark " mass. By Theory, this could be made up of microscopic singularities, Black Holes formed shortly after the Big Bang. We can create models to predict how much this would be:

Prediction: 23.87%

$\Omega_m$ 22.2 ± 2.6 (Prediction correct within 0.6 standard deviations)

This also predicts a changing speed of light, which can be seen in Type Ia supernova redshifts and laser ranging of the Moon. Why does this work not get more attention? New ideas, especially ideas ahead of their time, take time to be accepted. The inefficient neural net of humanity contains many old nodes that refuse to accept change. Thanks to talks and this blog, Theory is now known worldwide. The genie has escaped the bottle!