A Cosmological Slavnov-Taylor Identity

Abstract

We develop a method for treating the consistency relations of inflation that includes the full time-evolution of the state. This approach relies only on the symmetries of the inflationary setting, in particular a residual conformal symmetry in the spatial part of the metric, along with general properties which hold for any quantum field theory. As a result, the consistency relations that emerge, which are essentially the Slavnov-Taylor identities associated with this residual conformal symmetry, apply very generally: they are true of the full Green's functions, hold largely independently of the particular inflationary model, and can be used for arbitrary states. We illustrate these techniques by showing the form assumed by the standard consistency relation between the two and three-point functions for the primordial scalar fluctuations when they are in a Bunch-Davies state. But because we have included the full evolution of the state, this approach works for a general initial state as well and does not need to have assumed that inflation began in the Bunch-Davies state.

38 pages (published version, new material on initial states added)

References in corpus (4)

• Conformal Symmetries of Adiabatic Modes in Cosmology
• Consistency condition for inflation from (broken) conformal symmetry
• On the Initial State and Consistency Relations
• Renormalizing an initial state

Cited by in corpus (6)

• On the scalar consistency relation away from slow roll
• Soft limits in holographic cosmology
• On the Initial State and Consistency Relations
• General Covariance Constraints on Cosmological Correlators
• Inflation in Flatland
• The double-soft limit in cosmological correlation functions and graviton exchange effects