Non-local Entanglement and Fast Scrambling in De-Sitter Holography

We study holographic entanglement and information scrambling in de-Sitter (dS) space in the context of the DS/dS correspondence. We find that our previously identified non-local entanglement structure of dS vacua can be extended out of the time-reflection symmetric slice. We extend the geometry to a two-sided configuration and calculate the zero-time mutual information between two intervals on different sides when there is a localized shock wave in the bulk. Interestingly, we find that the information scrambling time saturates the fast scrambler bound proposed by Sekino and Susskind and that the shock wave renders a wormhole to be traversable. Furthermore, we calculate a two-sided out-of-time-ordered correlator (OTOC) in the late time regime and we see that, before scrambling, it exponentially grows with an exponent whose value saturates the maximal bound of chaos proposed by Maldacena, Shenker and Stanford. At the end, we provide an explanation why the exponential growing of the late-time OTOC with the maximal bound of chaos saturated and the traversability of the wormhole are simple results of the non-local entanglement structure and point out that this is a realization of the ER=EPR proposal.