Geodesic completeness and homogeneity condition for cosmic inflation
  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.
