The Cosmological Slavnov-Taylor Identity from BRST Symmetry in Single-Field Inflation

Abstract

The cosmological Slavnov-Taylor (ST) identity of the Einstein-Hilbert action coupled to a single inflaton field is obtained from the Becchi-Rouet-Stora-Tyutin (BRST) symmetry associated with diffeomorphism invariance in the Arnowitt-Deser-Misner (ADM) formalism. The consistency conditions between the correlators of the scalar and tensor modes in the squeezed limit are then derived from the ST identity, together with the softly broken conformal symmetry. Maldacena's original relations connecting the 2- and 3-point correlators at horizon crossing are recovered, as well as the next-to-leading corrections, controlled by the special conformal transformations.

38 pages, no figures. Corrected an error in the bispectrum relations, so that original Maldacena's results are now recovered. Added new sections on the extended discussions of the in-in formalism in the BRST approach and higher order corrections in the squeezed limit (special conformal transformations). Revised version accepted for publication in JCAP

References in corpus (6)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• On the consistency relation of the 3-point function in single field inflation
• Chaotic inflation, radiative corrections and precision cosmology
• The squeezed limit of the bispectrum in multi-field inflation
• A Cosmological Slavnov-Taylor Identity
• General Covariance Constraints on Cosmological Correlators

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• The Separate Universe Approach to Soft Limits
• Consistency relations in multi-field inflation
• Cosmological Correlators, In-In Formalism and Double Copy
• The Physical Content of Long Tensor Modes in Cosmology
• BRST Quantization of Cosmological Perturbations
• The double-soft limit in cosmological correlation functions and graviton exchange effects