Symmetries and Loops in Inflation

TL;DR

This paper proves that the curvature perturbation zeta remains conserved on superhorizon scales in single-field inflation, ensuring all correlators are time-independent at all loop orders, based on fundamental symmetries.

Contribution

It establishes the operator-level conservation of zeta in single-field inflation, linking it to locality, diffeomorphism invariance, and operator renormalization.

Findings

Zeta conservation holds as an operator statement.

All zeta-correlators are time independent at all loop orders.

The results connect conservation laws with symmetry principles and operator renormalization.

Abstract

In this paper, we prove that the superhorizon conservation of the curvature perturbation zeta in single-field inflation holds as an operator statement. This implies that all zeta-correlators are time independent at all orders in the loop expansion. Our result follows directly from locality and diffeomorphism invariance of the underlying theory. We also explore the relationship between the conservation of zeta, the single-field consistency relation and the renormalization of composite operators.