CMB from CFT

Abstract

During inflation, spacetime is approximately described by de Sitter space which is conformally invariant with the symmetry group SO(1,4). This symmetry can significantly constrain the quantum perturbations which arise in the inflationary epoch. We consider a general situation of single field inflation and show that the three point function involving two scalar modes and one tensor mode is uniquely determined, up to small corrections, by the conformal symmetries. Special conformal transformations play an important role in our analysis. Our result applies only to models where the inflaton sector also approximately preserves the full conformal group and shows that this three point function is a good way to test if special conformal invariance was preserved during inflation.

46 pages

References in corpus (13)

• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Holography from Conformal Field Theory
• Effective Field Theory for Inflation
• The Higher Spin/Vector Model Duality
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• Holography for inflation using conformal perturbation theory
• Holographic Non-Gaussianity
• Cosmological 3-point correlators from holography
• Consistency condition for inflation from (broken) conformal symmetry
• The Four-point Correlator in Multifield Inflation, the Operator Product Expansion and the Symmetries of de Sitter
• The Pursuit of Non-Gaussian Fluctuations in the Cosmic Microwave Background
• Non-Gaussianity as a Probe of the Physics of the Primordial Universe and the Astrophysics of the Low Redshift Universe

Cited by in corpus (105)

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• Late-time Structure of the Bunch-Davies De Sitter Wavefunction
• Cosmological Cutting Rules
• From AdS to dS Exchanges: Spectral Representation, Mellin Amplitudes and Crossing
• From dS to AdS and back
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• Building a Boostless Bootstrap for the Bispectrum
• Linking the Singularities of Cosmological Correlators
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• Renormalised 3-point functions of stress tensors and conserved currents in CFT
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• The Inflationary Wavefunction from Analyticity and Factorization
• From Planck data to Planck era: Observational tests of Holographic Cosmology
• Conformal $n$-point functions in momentum space
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• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• Cosmological Bootstrap in Slow Motion
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• Soft de Sitter Effective Theory
• Shapes of gravity: Tensor non-Gaussianity and massive spin-2 fields
• CFT Unitarity and the AdS Cutkosky Rules
• Parity violation in the scalar trispectrum: no-go theorems and yes-go examples
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• Consequences of Symmetries and Consistency Relations in the Large-Scale Structure of the Universe for Non-local bias and Modified Gravity
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• Conformal correlators as simplex integrals in momentum space
• Bootstrapping Large Graviton non-Gaussianities
• On the Symmetries of Cosmological Perturbations
• From Amplitudes to Contact Cosmological Correlators
• The Conformal Limit of Inflation in the Era of CMB Polarimetry
• High-Scale Inflation and the Tensor Tilt
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• Towards the higher point holographic momentum space amplitudes II: Gravitons
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
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• Dynamical Constraints on RG Flows and Cosmology
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• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
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• On the power spectrum of inflationary cosmologies dual to a deformed CFT
• Momentum space spinning correlators and higher spin equations in three dimensions
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• Multiple Soft Limits of Cosmological Correlation Functions
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• Constraining momentum space correlators using slightly broken higher spin symmetry
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• Multi-field inflation from holography
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• Renormalisation of IR divergences and holography in de Sitter
• Tensors and Spinors in de Sitter Space
• Equal-time Consistency Relations in the Large-Scale Structure of the Universe
• Opacity from Loops in AdS
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• Holographic inflation and the conservation of $\zeta$
• Momentum space CFT correlators for Hamiltonian truncation
• Improvement of energy-momentum tensor and non-Gaussianities in holographic cosmology
• Lectures on Holographic Space Time
• Holography for the very early Universe and the classic puzzles of Hot Big Bang cosmology
• Momentum space CFT correlators of non-conserved spinning operators
• Rational Wavefunctions in de Sitter Spacetime
• Holographic non-Gaussianities in general single-field inflation
• Inflation and Conformal Invariance: The Perspective from Radial Quantization
• Anyonic correlation functions in Chern-Simons matter theories
• Higher Spin de Sitter Hilbert Space
• Mixed Graviton and Scalar Bispectra in the EFT of Inflation: Soft Limits and Boostless Bootstrap
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• Holographic Fluctuations from Unitary de Sitter Invariant Field Theory
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