# Asymptotic Behavior of Cosmologies with $\Lambda >0$ in 2+1 Dimensions

## TL;DR

This paper analyzes the long-term evolution of 2+1 dimensional cosmological models with positive cosmological constant, showing they asymptotically resemble de Sitter space despite initial fluctuations and black hole formation.

## Contribution

It demonstrates, using Mean Curvature Flow, that such cosmologies asymptotically approach de Sitter space regardless of initial density fluctuations.

## Key findings

- Spatial slices reach infinite volume
- They asymptotically converge to de Sitter space
- Black hole formation does not prevent asymptotic de Sitter behavior

## Abstract

We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with a positive cosmological constant and matter satisfying the dominant and the strong energy conditions. If the spatial slices are compact with non-positive Euler characteristic and are initially expanding everywhere, then we prove that the spatial slices reach infinite volume, asymptotically converge on average to de Sitter and they become, almost everywhere, physically indistinguishable from de Sitter. This holds true notwithstanding the presence of initial arbitrarily-large density fluctuations and the formation of black holes.