Cosmology from the two-dimensional renormalization group acting as the Ricci flow

Abstract

The two-dimensional renormalization group acting as the Ricci flow $\Lambda \frac{\partial }{\partial \Lambda }{g}_{\mu \nu }=R_{\mu \nu }$ produces a specific 1+3 dimensional space-time metric which describes an expanding universe that starts with a big bang $a\sim t^{1/\sqrt{3}}$ then decelerates until $z=0.2$ then accelerates until ending at $t_{\max }=1.6t_H$ with a big blowup $a\sim (t_{\max }-t{)}^{-1/\sqrt{3}}$. The only free parameters are the overall time scale and the value of the present time $t_0$. These are fixed by the Hubble constant $H_0=t_H^{-1}$ and the present deceleration parameter $q(t_0)$. This crude calculation of cosmology omits all but the gravitational field. The only energy-momentum is purely gravitational dark matter and energy. This is a preliminary exploration towards a specific, comprehensive, testable calculation of cosmology from a fundamental theory in which physics is produced by a quantum version of the two-dimensional renormalization group.

v2 corrects one typo; 6 pages, 2 figures, supplementary material (a pdf file showing calculations and three SageMath notebooks performing numerical calculations)

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