Abstract
We discuss some implications of recent progress in understanding the black hole information paradox for complementarity in de Sitter space. Extending recent work by two of the authors, we describe a bulk procedure that allows information expelled through the cosmological horizon to be received by an antipodal observer. Generically, this information transfer takes a scrambling time t = H−1 log(SdS). We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static patches. The procedure also requires the presence of an (entangled) energy reservoir, created by the collection of Hawking modes from the cosmological horizon. We show how this procedure avoids a cloning paradox and comment on its implications.
Highlights
AdS eternal black hole, there are important differences
We begin with a short reminder of the thermofield double state and how isotropic shockwaves in de Sitter space can in principle allow the exchange of information between two antipodal observers
We will present a short summary of the status of complementarity in de Sitter space, briefly reminding the reader about the Page and scrambling times, as well as how the firewall and cloning paradoxes are avoided in the AdS eternal black hole context [9, 21, 31,32,33]
Summary
To begin let us remind the reader that the AdS black hole thermofield double state has a clear analogue in (semi-classical) de Sitter space [22]. The vacuum expectation value of any operator O with support in just one of the static patches can be computed using the reduced density matrix: Ψ|O(xS)|Ψ = TrS(O(xS)ρS), where the South Pole reduced density matrix ρS is obtained by tracing the thermofield double state over the North Pole region ρS ≡ TrN |Ψ Ψ| This means the expectation value remains invariant under the full set of de Sitter isometries. Once the thermofield double state is prepared this way (for instance at the global timeslice t = 0), non-trivial time evolution can be generated by the sum (instead of the difference) of the static patch Hamiltonians, introducing additional time-dependent phases in the Schrödinger state We will use this entangled static patch set-up to argue, as for the AdS eternal black hole, that any message sent through the de Sitter horizon can be received by the antipodal observer, if a shockwave is released after at least a scrambling time. Having outlined the general idea let us introduce a few more details, starting with some results of [20]
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