Entanglement between two gravitating universes

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for $n^{\text{th}}$ R\'enyi entropy includes a wormhole between $n$ copies of gravitating universe, leading to standard "island formula" entanglement consistent with unitarity quantum information. both contain gravitational corrections this configuration lead violation unitarity. However, is now dominated by novel $2n$ boundaries connecting replica universes. The analytic continuation contribution involves quotient $\mathbb{Z}_n$ symmetry, giving cylinder large, has effective description as "swap wormhole", geometry which are glued together "swaperator". This allows precise computation generalized entropy-like formula entropy. extremal surface computing lives on Lorentzian cylinder/swap wormhole, connected Cauchy slice stretching -- realization ER=EPR idea. new restores