A timelike entangled island at the initial singularity in a JT FLRW ($Λ>0$) universe

Abstract: It has been argued that there are no islands in FLRW cosmologies with $\Lambda>0$ and $k=0$ arXiv:2008.01022. We argue that there is a timelike separated island at the initial singularity, and it will resolve the cosmological information paradox. The information about the particles that went beyond the horizon is not lost for our observer. By measuring Hawking radiation, we can get that information from the past when those particles were near the initial singularity. Similar to how islands inside black holes violate locality, we observe a violation of causality or noncausality but only at the initial singularity, possibly the only region where it is acceptable. We start with a review of timelike entanglement. We will follow an approach similar to the one followed in arXiv:2104.00006 for normal islands. In the end, we conjecture a generalization of the Ryu-Takayanagi or QES prescription for the case of bulk timelike entanglement in dS/CFT correspondence and comment on the emergence of time in dS/CFT correspondence.