Tall tales from de Sitter space I: Renormalization group flows

Abstract

We study solutions of Einstein gravity coupled to a positive cosmological constant and matter, which are asymptotically de Sitter and homogeneous. Regarded as perturbations of de Sitter space, a theorem of Gao and Wald implies that generically these solutions are `tall,' meaning that the perturbed universe lives through enough conformal time for an entire spherical Cauchy surface to enter any observer's past light cone. Such observers will realize that their universe is spatially compact. An interesting fact, which we demonstrate with an explicit example, is that this Cauchy surface can have arbitrarily large volume for fixed asymptotically de Sitter behavior. Our main focus is on the implications of tall universes for the proposed dS/CFT correspondence. Particular attention is given to the associated renormalization group flows, leading to a more general de Sitter `c-theorem.' We find, as expected, that a contracting phase always represents a flow towards the infrared, while an expanding phase represents a `reverse' flow towards the ultraviolet. We also discuss the conformal diagrams for various classes of homogeneous flows.

32 pages, 16 figures, references added

References in corpus (17)

• Eternal Black Holes in AdS
• The dS/CFT Correspondence
• Inflationary spacetimes are not past-complete
• Quantum Gravity In De Sitter Space
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Conformal Vacua and Entropy in de Sitter Space
• Inflation and the dS/CFT Correspondence
• The dS/CFT Correspondence and the Big Smash
• Deconstructing de Sitter
• The "physical process" version of the first law and the generalized second law for charged and rotating black holes
• Some Aspects of the de Sitter/CFT Correspondence
• Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
• Vacuum States and the S-Matrix in dS/CFT
• Check of the Mass Bound Conjecture in the de Sitter Space
• The Asymptotic Dynamics of de Sitter Gravity in three Dimensions
• Note on Gauge Theories on M/G and the AdS/CFT Correspondence
• Note on Holographic RG Flow in String Cosmology

Cited by in corpus (61)

• The dS/CFT Correspondence and the Big Smash
• The Phantom Divide in String Gas Cosmology
• Interacting Quantum Field Theory in de Sitter Vacua
• Elliptic de Sitter Space: dS/Z_2
• Exact asymptotically flat charged hairy black holes with a dilaton potential
• Exploring de Sitter Space and Holography
• SD-brane gravity fields and rolling tachyons
• The central dogma and cosmological horizons
• Inflation without a beginning: a null boundary proposal
• Reissner-Nordstrom-de Sitter black hole, planar coordinates and dS/CFT
• Non-Gaussian Inflationary Perturbations from the dS/CFT Correspondence
• Accelerating Universes and String Theory
• Chaos and complementarity in de Sitter space
• Alpha-states in de Sitter space
• Hologravity
• Spontaneous decompactification
• Inflationary Perturbations from Deformed CFT
• Holographic Complexity in dS${}_{d+1}$
• Entropic N-bound and Maximal Mass Conjecture Violations in Four Dimensional Taub-Bolt(NUT)-dS Spacetimes
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Inflation and Braneworlds: Degeneracies and Consistencies
• On higher derivative gravity, c-theorems and cosmology
• Exact hairy black brane solutions in $Ad{S}_5$ and holographic RG flows
• Bouncing Braneworlds Go Crunch!
• dS-Holographic C-Functions with a Topological, Dilatonic Twist
• de Sitter entropy from conformal field theory
• Tall tales from de Sitter space II: Field theory dualities
• Encoding beyond cosmological horizons in de Sitter JT gravity
• Entropy and Mass Bounds of Kerr-de Sitter Spacetimes
• Vacuum decay in the Lorentzian path integral
• Cosmological Solutions on Atiyah-Hitchin Space in Five Dimensional Einstein-Maxwell-Chern-Simons Theory
• Cosmological solutions in five dimensional Einstein-Maxwell-dilaton theory
• Stringy Instability of Topologically Non-Trivial Ads Black Holes and of desitter S-Brane Spacetimes
• The Most Probable Size of the Universe
• On the structure of asymptotically de Sitter and anti-de Sitter spaces
• Exact convoluted solutions in higher-dimensional Einstein-Maxwell theory
• Massive Gravitino Propagator in Maximally Symmetric Spaces and Fermions in dS/CFT
• Of Bounces, Branes and Bounds
• New class of exact solutions to Einstein-Maxwell-dilaton theory on four-dimensional Bianchi type IX geometry
• Horizon complementarity in elliptic de Sitter space
• Cosmological Solutions in Five Dimensional Minimal Supergravity
• Exact helicoidal and catenoidal solutions in Einstein-Maxwell theory
• Alpha-Vacua, Black Holes, and AdS/CFT
• The Strong Energy Condition and the S-Brane Singularity Problem
• Probing Planckian physics in de Sitter space with quantum correlations
• Bianchi IX geometry and the Einstein-Maxwell theory
• The Geometry of The Entropic Principle and the Shape of the Universe
• Bad News on the Brane
• Holography and quantum states in elliptic de Sitter space
• Big Bangs and Bounces on the Brane
• Horizon causality from holographic scattering in asymptotically dS${}_3$
• Mirage resolution of cosmological singularities
• Exact spectrum of scalar field perturbations in a radiation deformed closed de Sitter universe
• Exact Solutions to Einstein-Maxwell theory on Eguchi-Hanson Space
• Remark About dS/CFT Correspondence
• Comments on cosmological RG flows
• RG flows in de Sitter: c-functions and sum rules
• de Sitter symmetries and inflationary scalar-vector models
• Dwelling on de Sitter
• Singularities in and Stability of Ooguri-Vafa-Verlinde Cosmologies
• The clash between de Sitter and anti-de Sitter space