Cosmology as a CFT${}_1$

Abstract

We show that the simplest FLRW cosmological system consisting in the homogeneous and isotropic massless Einstein-Scalar system enjoys a hidden conformal symmetry under the 1D conformal group $SL(2,\mathbb{R})$ acting as Mobius transformations in proper time. This invariance is made explicit through the mapping of FLRW cosmology onto conformal mechanics. On the one hand, we identify the corresponding conformal Noether charges, as combinations of the Hamiltonian scalar constraint, the extrinsic curvature and the 3D volume, which form a closed $sl(2,\mathbb{R})$ Lie algebra. On the other hand, this approach allows to write FLRW cosmology in terms of a AdS${}_2$ phase space and a Schwarzian action. Preserving this conformal structure at the quantum level fixes the ordering ambiguities in the Wheeler-de Witt quantization and allows to formulate FLRW quantum cosmology as a CFT${}_1$. We show that the CFT two-points correlator is realized as the overlap of the evolution in proper time of cosmological coherent wave-packets. In particular, the two-points function is built from a vacuum state which, although not conformally invariant, coincides with the cosmological vacuum annihilated by the scalar constraint. These results suggest new perspectives in classical and quantum cosmology, among which the possibility to apply the conformal bootstrap program to quantize cosmological backgrounds.

arXiv comment44 pages, minor modifications in the introduction and discussion, as well as additional references. This version matches the one accepted in JHEP

References in corpus (100)

• Thermodynamics of Spacetime: The Einstein Equation of State
• The dS/CFT Correspondence
• The Kerr/CFT Correspondence
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Chaos in AdS${}_2$ holography
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Conformal Field Theory Interpretation of Black Hole Quasi-normal Modes
• The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Near-horizon symmetries of extremal black holes
• Predictions from Quantum Cosmology
• Entropy from Conformal Field Theory at Killing Horizons
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Hidden Conformal Symmetry of the Kerr Black Hole
• Solving the Schwarzian via the Conformal Bootstrap
• Inflation and de Sitter Thermodynamics
• Universal Low-Energy Dynamics for Rotating Black Holes
• Classification of near-horizon geometries of extremal black holes
• Black Hole Superradiance From Kerr/CFT
• Lorentzian Quantum Cosmology
• AdS${}_2$ holography and the SYK model
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Quantum cosmology: a review
• Vacuum States for AdS_2 Black Holes
• Is There Really a de Sitter/CFT Duality
• Homogeneous cosmologies as group field theory condensates
• Spacetime structure near generic horizons and soft hair
• Towards a Big Crunch Dual
• Holographic Description of AdS Cosmologies
• Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter
• The Schwarzian Theory - Origins
• Near-Horizon Conformal Symmetry and Black Hole Entropy
• Conformal quantum mechanics as the CFT${}_1$ dual to AdS${}_2$
• Cargese Lectures on the Kerr/CFT Correspondence
• Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
• The Schwarzian Theory - A Wilson Line Perspective
• Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
• Anomaly in conformal quantum mechanics: From molecular physics to black holes
• The universe as a quantum gravity condensate
• Bouncing cosmologies from quantum gravity condensates
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• Central Charge for AdS_2 Quantum Gravity
• Dynamical coherent states and physical solutions of quantum cosmological bounces
• On the Quantum Resolution of Cosmological Singularities using AdS/CFT
• Tunneling wave function of the universe
• Superconformal Black Hole Quantum Mechanics
• Menagerie of AdS${}_2$ boundary conditions
• On CFT and Quantum Chaos
• The Kerr/CFT correspondence and its extensions: a comprehensive review
• Chaos in Quantum Cosmology
• Gravity Waves from Kerr/CFT
• A Matrix Model for AdS2
• Conformal structure of the Schwarzschild black hole
• Quantum Cosmology: Effective Theory
• Black hole versus cosmological horizon entropy
• w_{\infty} Algebras, Conformal Mechanics, and Black Holes
• Effective Conformal Descriptions of Black Hole Entropy
• Black Hole Thermodynamics from Near-Horizon Conformal Quantum Mechanics
• Liouville theory beyond the cosmological horizon
• High Energy Physics Signatures from Inflation and Conformal Symmetry of de Sitter
• Fine-Grained Chaos in $Ad{S}_2$ Gravity
• A 2d/1d Holographic Duality
• Conformal Blocks for the 4-Point Function in Conformal Quantum Mechanics
• The Thiemann Complexifier and the CVH algebra for Classical and Quantum FLRW Cosmology
• NHEG Mechanics: Laws of Near Horizon Extremal Geometry (Thermo)Dynamics
• Extremal Rotating Black Holes in the Near-Horizon Limit: Phase Space and Symmetry Algebra
• $Ad{S}_2$ dilaton gravity from reductions of some nonrelativistic theories
• Hidden Conformal Symmetry and Quasi-normal Modes
• Notes on $\widetilde{\mathrm{SL}}(2,\mathbb{R})$ representations
• Coarse graining as a representation change
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Modular discretization of the AdS2/CFT1 Holography
• Polymer Quantum Cosmology: Lifting quantization ambiguities using a $SL(2,\mathbb{R})$ conformal symmetry
• Effective Conformal Descriptions of Black Hole Entropy: A Review
• Logarithmic corrections to black hole entropy from Kerr/CFT
• Group theoretical Quantization of Isotropic Loop Cosmology
• Cosmological horizons, Noether charges and entropy
• Generalized hidden Kerr/CFT
• Conformal mechanics on rotating Bertotti-Robinson spacetime
• Conformal Symmetries of FRW Accelerating Cosmologies
• Rational deformations of conformal mechanics
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry
• Conformal Mechanics and the Virasoro Algebra
• Towards causal patch physics in dS/CFT
• Inflation and Conformal Invariance: The Perspective from Radial Quantization
• Correlation functions in the Schwarzian theory
• Implications of Conformal Symmetry in Quantum Mechanics
• Note on correlation functions in conformal quantum mechanics
• Inflationary Cosmology, Diffeomorphism Group of the Line and Virasoro Coadjoint Orbits
• A Realization of the infinite dimensional Symmetries of Conformal Mechanics
• The Interpretation of Quantum Cosmology and the Problem of Time
• Horizon temperature on the real line
• Quantum conformal mechanics
• Quantum cosmology for the 21st century: A debate
• On the geometry of conformal mechanics
• Conformal quantum mechanics and holography in noncommutative space-time
• Black holes and conformal mechanics
• A note on the infinite-dimensional symmetries of classical hamiltonian systems

Cited by in corpus (1)

• The Cosmological Constant from Conformal Transformations: Möbius Invariance and Schwarzian Action