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Aspects of Symmetry in de Sitter Space

We study various aspects of symmetry in four-dimensional de Sitter space (dS4). The asymptotic symmetry group at future null infinity (I+) of dS4 is shown to be given by the group of three-dimensional di↵eomorphisms acting on I+. However, for physics relevant to an eternal observatory in dS4, we should instead impose unconventional future boundary conditions at I+. These boundary conditions violate conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. As the next step, we study the relevant dynamics in quantum dS4 by illuminating some previously inaccessible aspects of the dS/CFT dictionary in the context of the higher spin dS4/CFT3 correspondence relating Vasiliev’s higher-spin gravity on dS4 to a Euclidean Sp(N) CFT3. We found that CFT3 states created by operator insertions are found to be dual to (anti) quasinormal modes (QNM) in the bulk. A R-norm is defined on the R3 bulk Hilbert space and shown for the scalar case to be equivalent to both the Zamolodchikov and pseudounitary C-norm of the Sp(N) CFT3. The QNMs are found to lie in two complex highest-weight representations of the dS4 isometry group and form a complete orthogonal basis with respect to the R-norm. The conventional Euclidean vacuum may be defined as the state annihilated by half of the QNMs, and the Euclidean Green function is obtained from a simple mode sum. Finally, as a step towards understanding non-linear dynamics of dS4 we study both linear and non-linear deformations of dS4 which leave the induced conformal metric and trace of the extrinsic curvature unchanged for a fixed hypersurface. These deformations are required to be regular at the future horizon of the static patch observer. When the slices are arbitrarily close to the cosmological horizon, the finite deformations are characterized by solutions to the incompressible Navier-Stokes equation.