# Geodesic completeness and homogeneity condition for cosmic inflation

Research paper by Aindriu Conroy, Alexey S. Koshelev, Anupam Mazumdar

Indexed on: 26 Aug '14Published on: 26 Aug '14Published in: General Relativity and Quantum Cosmology

#### 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.