# Topology and singularities in cosmological spacetimes obeying the null energy condition

## TL;DR

This paper explores how the topology of Cauchy surfaces in certain cosmological spacetimes influences the presence of past singularities, using advanced topology and minimal surface techniques.

## Contribution

It establishes a precise link between Cauchy surface topology and past singularities in 3+1 dimensional spacetimes obeying the null energy condition.

## Key findings

- Topology of Cauchy surfaces determines singularity occurrence.
- Refinement of Penrose singularity theorem.
- Application of minimal surface existence results.

## Abstract

We consider globally hyperbolic spacetimes with compact Cauchy surfaces in a setting compatible with the presence of a positive cosmological constant. More specifically, for 3+1 dimensional spacetimes which satisfy the null energy condition and contain a future expanding compact Cauchy surface, we establish a precise connection between the topology of the Cauchy surfaces and the occurrence of past singularities. In addition to (a refinement of) the Penrose singularity theorem, the proof makes use of some recent advances in the topology of 3-manifolds and of certain fundamental existence results for minimal surfaces.