Geodesic completeness and homogeneity condition for cosmic inflation

TL;DR

This paper explores how a non-local extension of General Relativity can simultaneously resolve issues of geodesic completeness and homogeneity in cosmic inflation, addressing singularities and initial conditions.

Contribution

It demonstrates that a non-local modification of GR can address both geodesic completeness and homogeneity conditions in inflationary cosmology.

Findings

Non-local GR extension resolves past geodesic incompleteness.

Addresses homogeneity condition for inflation.

Satisfies null energy condition with matter sources.

Abstract

There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past geodesic completeness of the inflationary trajectory due to the presence of a cosmological singularity, and the other one is related to the homogeneity condition required to inflate a local space-time patch of the universe. We will show that both the problems have a common origin, arising from how the causal structure of null and timelike geodesics are structured within GR. In particular, we will show how a non-local extension of GR can address both problems, while satisfying the null energy condition for the matter sources.