Consistency Relations for the Conformal Mechanism

Abstract

We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate (N+1)-point correlation functions with a soft external Goldstone to N-point functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel one-loop contribution to the four-point function, relevant for the stochastic scale-dependent bias and CMB mu-distortion.

34 pages, 3 figures. v2: minor changes, version appearing in JCAP

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Cited by in corpus (36)

• An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology
• Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation
• Imprints of Massive Primordial Fields on Large-Scale Structure
• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• Ward Identities for Scale and Special Conformal Transformations in Inflation
• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• Inflationary tensor fossils in large-scale structure
• Slavnov-Taylor Identities for Primordial Perturbations
• Distinctive signatures of space-time diffeomorphism breaking in EFT of inflation
• Shift Symmetries in (Anti) de Sitter Space
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• Large-scale tidal effect on redshift-space power spectrum in a finite-volume survey
• Symmetry Constraints in Inflation, $\alpha$-vacua, and the Three Point Function
• Multiple Soft Limits of Cosmological Correlation Functions
• Gaugid inflation
• On the Initial State and Consistency Relations
• Correlating CMB Spectral Distortions with Temperature: what do we learn on Inflation?
• General quadrupolar statistical anisotropy: Planck limits
• Inflation and Conformal Invariance: The Perspective from Radial Quantization
• Revisiting constraints on (pseudo)conformal Universe with Planck data
• Quadratic Isocurvature Cross-Correlation, Ward Identity, and Dark Matter
• On holography for (pseudo-)conformal cosmology
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• Effect of intermediate Minkowskian evolution on CMB bispectrum
• Holography for a Non-Inflationary Early Universe
• Conformal Universe as false vacuum decay
• Towards conformal cosmology
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• Amplifying the Cosmological Collider with Ghost Spectators
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• Non-relativistic Cosmological Collider Signals
• Weakly Broken Galileon Symmetry in Cosmology