Islands in FRW Cosmologies

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.