Islands in FRW Cosmologies

TL;DR

This paper investigates the existence of island regions in Friedmann-Robertson-Walker cosmologies with radiation, cosmological constant, and curvature, finding that negative cosmological constant is crucial for island formation.

Contribution

It identifies conditions under which island regions can exist in FRW cosmologies, highlighting the role of negative cosmological constant and providing analytic and numerical results.

Findings

In closed universes, the entire Cauchy slice forms an island.

Finite-sized island regions appear at turnaround times for certain parameters.

Negative cosmological constant is essential for the existence of islands.

Abstract

We search for candidate island regions in FRW cosmologies supported by radiation, cosmological constant $\Lambda$, and non-zero spatial curvature. The radiation is assumed to be in a thermal state. We apply the necessary conditions introduced in [arXiv:2008.01022]. Both for the open and closed universes with $\Lambda<0$, the Friedmann equation admits recollapsing solutions with a time-symmetric slice. In the case of closed universes, there is always an island that is the whole Cauchy slice. However, for $\Lambda<0$, we also find another finite-sized candidate island region, in the middle of the spacetime, at the turnaround time. In the case of the open universes, we only find a candidate island region for $\Lambda<0$, that appears at the turnaround time. It starts from a finite value of the radial coordinate and extends to infinity. Looking at both open and closed universes, we conclude that the key ingredient that allows the existence of islands is the negative cosmological constant. We provide analytic results along the time-symmetric slices and support our results with numerics in the whole spacetime.