# CMC foliations of open spacetimes asymptotic to open Robertson-Walker spacetimes

## TL;DR

This paper proves the existence and uniqueness of constant mean curvature foliations in open, asymptotically Robertson-Walker spacetimes, establishing a smooth time function and connecting to models of the universe's development.

## Contribution

It demonstrates the existence and uniqueness of CMC foliations in open spacetimes asymptotic to Robertson-Walker universes, with implications for cosmological models.

## Key findings

- Existence of unique CMC foliation in asymptotic open spacetimes
- The mean curvature function is a smooth time function
- Application to models reflecting the universe's development

## Abstract

We consider open globally hyperbolic spacetimes $N$ of dimension $n+1$, $n\ge 3$, which are spatially asymptotic to a Robertson-Walker spacetime or an open Friedmann universe with spatial curvature $\tilde\kappa = 0,-1$ and prove, under reasonable assumptions, that there exists a unique foliation by hypersurfaces of constant mean curvature and that the mean curvature function $\tau$ is a smooth time function if $N$ is smooth. Moreover, among the Friedmann universes which satisfy the necessary conditions are those that reflect the present assumptions of the development of the universe.