Kavli Affiliate: Yasunori Nomura
| First 5 Authors: Vijay Balasubramanian, Yasunori Nomura, Tomonori Ugajin, ,
| Summary:
Multiple lines of evidence suggest that the Hilbert space of an isolated de
Sitter universe is one dimensional but can appear larger when probed by a
gravitating observer. To test this idea, we compute the von Neumann entropy of
a field theory in a two-dimensional de Sitter universe which is entangled in a
thermal-like state with the same field theory on a disjoint, asymptotically
anti-de Sitter (AdS) black hole. Previously, it was shown that the replica
trick for computing the entropy of such entangled gravitating systems requires
the inclusion of a non-perturbative effect in quantum gravity — novel
wormholes connecting the two spaces. Here we show that: (a) the expected
wormholes connecting de Sitter and AdS universes exist, avoiding a no-go
theorem via the presence of sources on the AdS boundary; (b) the entanglement
entropy vanishes if the nominal entropy of the de Sitter cosmological horizon
(S_dS = A_horizon^dS / 4G_N) is less than the entropy of the AdS black hole
horizon (S_BH = A_horizon^AdS / 4G_N), i.e., S_dS < S_BH; (c) the entanglement
entropy is finite when S_dS > S_BH. Thus, the de Sitter Hilbert space is
effectively nontrivial only when S_dS > S_BH. The AdS black hole we introduce
can be regarded as an “observer” for de Sitter space. In this sense, our
result is a non-perturbative generalization of the recent perturbative argument
that the algebra of observables on the de Sitter static patch becomes
nontrivial in the presence of an observer.
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