A Cosmological Slavnov-Taylor Identity

TL;DR

This paper derives a general set of consistency relations for inflationary correlators based on residual conformal symmetry, applicable to arbitrary states and full time evolution, extending previous results limited to specific initial conditions.

Contribution

It introduces a method using Slavnov-Taylor identities from residual conformal symmetry to derive inflationary consistency relations valid for any quantum state and full dynamical evolution.

Findings

Consistency relations hold for arbitrary initial states.

Relations are derived from residual conformal symmetry.

Method applies to full Green's functions and evolution.

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.