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 (14)

• Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation
• DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios
• Inflationary tensor fossils in large-scale structure
• 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
• General quadrupolar statistical anisotropy: Planck limits
• Revisiting constraints on (pseudo)conformal Universe with Planck data
• Holography for a Non-Inflationary Early Universe
• Conformal Universe as false vacuum decay
• Perturbations on and off de Sitter brane in anti-de Sitter bulk
• Primordial fluctuations in extended Liouville theory
• Weakly Broken Galileon Symmetry in Cosmology