Higher Spin de Sitter Hilbert Space

We propose acomplete microscopic definition of the Hilbert space of minimal higher spin deSitter quantum gravity and its Hartle-Hawking vacuum state. The fundamentaldegrees of freedom are 2N  bosonic fields living on thefuture conformal boundary, where N  is proportional to the de Sitterhorizon entropy. The vacuum state is normalizable. The model agrees inperturbation theory with expectations from a previously proposed dS-CFTdescription in terms of a fermionic Sp(N) model, but it goes beyond this, bothin its conceptual scope and in its computational power. In particular itresolves the apparent pathologies affecting the Sp(N) model, and it provides anexact formula for late time vacuum correlation functions. We illustrate this bycomputing probabilities for arbitrarily large field excursions, and by givingfully explicit examples of vacuum 3- and 4-point functions. We discuss bulkreconstruction and show the perturbative bulk QFT canonical commutationsrelations can be reproduced from the fundamental operator algebra, but only upto a minimal error term ∼e −O(N)   , and only if the operators arecoarse grained in such a way that the number of accessible "pixels"is less than O(N). Independent of this, we show that upon gauging the higher spin symmetry group, one is left with 2N physical degrees of freedom, and that all gauge invariant quantities can becomputed by a 2N × 2N  matrix model. This suggests aconcrete realization of the idea of cosmological complementarity.