A Brief History of Curvature

TL;DR

This paper explores the evolution of the Ricci scalar curvature in the universe from inflation to today, highlighting how early universe phase transitions leave significant, detectable imprints on cosmic curvature.

Contribution

It provides a detailed analysis of how the thermal history and phase transitions of the early universe affect the Ricci scalar curvature over cosmic time.

Findings

Significant imprints on scalar curvature from QCD and electroweak transitions.

Imprints can be of either sign and are much larger than naive extrapolations.

Curvature evolution reflects the universe's thermal and phase transition history.

Abstract

The trace of the stress-energy tensor of the cosmological fluid, proportional to the Ricci scalar curvature in general relativity, is determined on cosmic scales for times ranging from the inflationary epoch to the present day in the expanding Universe. The post-inflationary epoch and the thermal history of the relativistic fluid, in particular the QCD transition from asymptotic freedom to confinement and the electroweak phase transition, leave significant imprints on the scalar curvature. These imprints can be of either sign and are orders of magnitude larger than the values that would be obtained by naively extrapolating the pressureless matter of the present epoch back into the radiation-dominated epoch.