Finite Features of Quantum De Sitter Space

Abstract

We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of black holes. We point out differences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS${}_2\times S^2$ space and a dS${}_4$ interior are compatible with the null energy condition, albeit with a non-standard decreasing radial size of $S^2$. The putative holographic dual of an asymptotic AdS${}_2$ spacetime is comprised of a finite number of degrees of freedom. From a Euclidean perspective we consider the gravitational path integral for fields over compact manifolds. In two-dimensions, we review Polchinski's BRST localisation of Liouville theory and propose a supersymmetric extension of timelike Liouville theory which exhibits supersymmetric localisation. We speculate that localisation of the Euclidean gravitational path integral is a reflection of a finite number of degrees of freedom in a quantum de Sitter universe.

20 pages plus appendices, published version including introduction + comment on fluid/gravity picture

References in corpus (19)

• Towards a derivation of holographic entanglement entropy
• An Algebra of Observables for de Sitter Space
• Analyticity and Unitarity for Cosmological Correlators
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• Towards a quantum theory of de Sitter space
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• Nonperturbative black hole entropy and Kloosterman sums
• Entanglement in De Sitter Space
• Holographic Complexity and de Sitter Space
• Constructing AdS_2 flow geometries
• Three-dimensional de Sitter horizon thermodynamics
• Sphere and disk partition functions in Liouville and in matrix integrals
• Density matrices in quantum gravity
• Some Thoughts on the Quantum Theory of de Sitter Space
• The initial boundary value problem and quasi-local Hamiltonians in General Relativity
• A Compendium of Sphere Path Integrals
• One-dimensional Quantum Gravity and the Schwarzian theory
• 2D quantum gravity partition function on the fluctuating sphere
• Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions

Cited by in corpus (12)

• The Cosmological Switchback Effect
• Complex geodesics in de Sitter space
• Keeping matter in the loop in dS${}_3$ quantum gravity
• A microscopic realization of dS${}_3$
• Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging
• Late-Time Correlators and Complex Geodesics in de Sitter Space
• dS${}_2$ Supergravity
• Flat space gravity at finite cutoff
• Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime
• The Cosmological Switchback Effect II
• Unconventional conformal invariance of maximal depth partially massless fields on $d{S}_4$ and its relation to complex partially massless SUSY
• JT Gravity in de Sitter Space and Its Extensions