The Ricci flow and the early universe

DOI10.1016/J.AOP.2023.169452arXiv2112.00218OpenAlexW4386003613MaRDI QIDQ6087313

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Publication date: 15 November 2023

Published in: Annals of Physics (Search for Journal in Brave)

Abstract: A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out the local small irregularities and makes the universe a homogeneous and isotropic Friedman-Robertson-Walker metric, but also develops a local singularity at the physical-time origin. Due to the phenomenological suppression of the non-Gaussian primordial perturbations, we assume the validity of the Ricci flow applying to the high curvature region near the local singularity of the very early universe. The no-local-collapsing theorem of Perelman ensures the existence of a canonical neighborhood around the large curvature pinching point, which resembles a gradient shrinking Ricci soliton (GSRS) solution of the Ricci flow. The GSRS reproduces an exact inflationary deSitter universe near the singularity at the leading order. The slow roll parameters are calculated by a small deviation from the singular flow-time via the Ricci flow, and primordial perturbations are also studied on the GSRS background, the power spectrum of the scalar perturbation agrees with present observations, and the one of the tensor perturbation is predicted too small to be detected than the standard inflation.

Full work available at URL: https://arxiv.org/abs/2112.00218

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Mathematics Subject Classification ID

Astronomy and astrophysics (85-XX) Relativity and gravitational theory (83-XX)