# Criticality of inhomogeneous Nariai-like cosmological models

## TL;DR

This paper constructs and analyzes inhomogeneous vacuum solutions with positive cosmological constant, revealing oscillatory dynamics at the boundary between collapse and expansion, using both analytical and numerical methods.

## Contribution

It introduces new inhomogeneous solutions generalizing the Nariai model and explores their oscillatory behavior through combined analytical and numerical approaches.

## Key findings

- Discovery of oscillatory dynamics in inhomogeneous Nariai-like models
- Analytical and numerical evidence supporting the oscillatory behavior
- Solutions at the threshold between collapse and exponential expansion

## Abstract

In this paper, we construct and study solutions of Einstein's equations in vacuum with a positive cosmological constant which can be considered as inhomogeneous generalizations of the Nariai cosmological model. Similar to this Nariai spacetime, our solutions are at the borderline between gravitational collapse and de-Sitter-like exponential expansion. Our studies focus in particular on the intriguing oscillatory dynamics which we discover. Our investigations are carried out both analytically (using heuristic mode analysis arguments) and numerically (using the numerical infrastructure recently introduced by us).