Cosmologies, singularities and quantum extremal surfaces

Following arXiv:2012.07351 [hep-th], we study quantum extremal surfaces in various families of cosmologies with Big-Crunch singularities, by extremizing the generalized entropy in 2-dimensional backgrounds which can be thought of as arising from dimensional reduction. Focussing first on the isotropic $AdS$ Kasner case, introducing a spatial regulator enables relating the locations in time of the quantum extremal surface and the observer. This shows that the quantum extremal surface lags behind the observer location. A potential island-like region, upon analysing more closely near the island boundary, turns out to be inconsistent. Similar results arise for other holographic cosmologies. We then study certain families of null Kasner singularities where we find that the quantum extremal surface can reach the near singularity region although the on-shell generalized entropy is generically singular. We also study other cosmologies including de Sitter (Poincare slicing) and FRW cosmologies under certain conditions.