Ricci flow for homogeneous compact models of the universe

TL;DR

This paper derives explicit Ricci flow solutions for homogeneous 3-sphere models of the universe using quaternions, analyzing their collapse and expansion behaviors.

Contribution

It provides a novel quaternion-based derivation of the Ricci tensor and explicit solutions for Ricci flow in homogeneous spherical models.

Findings

Explicit Ricci flow solutions for 3-sphere models

Analysis of collapse and expansion dynamics

Interplay of Ricci tensor components during evolution

Abstract

Using quaternions, we give a concise derivation of the Ricci tensor for homogeneous spaces with topology of the 3-dimensional sphere. We derive explicit and numerical solutions for the Ricci flow PDE and discuss their properties. In the collapse (or expansion) of these models, the interplay of the various components of the Ricci tensor are studied. We dedicate this paper to honor the work of Josh Goldberg.