English

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

Cosmology and Nongalactic Astrophysics 2020-05-13 v2 General Relativity and Quantum Cosmology High Energy Physics - Theory Differential Geometry

Abstract

The two-dimensional renormalization group acting as the Ricci flow ΛΛgμν=Rμν\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 at1/3a \sim t^{\scriptscriptstyle 1/\sqrt3} then decelerates until z=0.2z=0.2 then accelerates until ending at tmax=1.6tHt_{\max}=1.6\,t_{H} with a big blowup a(tmaxt)1/3a \sim (t_{\max}-t)^{\scriptscriptstyle -1/\sqrt3}. The only free parameters are the overall time scale and the value of the present time t0t_{0}. These are fixed by the Hubble constant H0=tH1H_{0}=t_{H}^{-1} and the present deceleration parameter q(t0)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.

Keywords

Cite

@article{arxiv.1909.01374,
  title  = {Cosmology from the two-dimensional renormalization group acting as the Ricci flow},
  author = {Daniel Friedan},
  journal= {arXiv preprint arXiv:1909.01374},
  year   = {2020}
}

Comments

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

R2 v1 2026-06-23T11:04:29.524Z