Pure de Sitter space and the island moving back in time

Observers in de Sitter space can only access the space up to their cosmological horizon. Assuming thermal equilibrium, we use the quantum Ryu-Takayanagi or island formula to compute the entanglement entropy between the states inside the cosmological horizon and states outside, as a function of time. We obtain a Page curve that is bound at a value corresponding to the Gibbons-Hawking entropy. At this transition an 'island' forms, which is in a significantly different location as compared to when considering black hole horizons and even moves back in time. These differences turn out to be essential for non-violation of the no-cloning theorem in combination with entanglement wedge reconstruction. This consideration furthermore introduces the need for a scrambling time, the entropy dependence of which turns out to coincide with what is expected for black holes. The model we employ has pure three-dimensional de Sitter space as a solution. We dimensionally reduce to two dimensions in order to take into account semi-classical effects. Nevertheless, we expect the aforementioned qualitative features of the island to persist in higher dimensions.