Effective Field Theory and In-In Correlators

TL;DR

This paper investigates how effective field theory and the Wilsonian renormalization group apply to in-in correlation functions in both flat and de Sitter spaces, revealing additional localized terms needed for accurate matching.

Contribution

It demonstrates the necessity of additional localized terms at measurement times in EFT correlators and explores their origin via exact RG in both flat and de Sitter spacetimes.

Findings

Additional localized terms are required for matching short- and long-distance correlators.

Explicit demonstration of matching in-in correlators in flat space with EFT results.

Local terms tend to redshift away in de Sitter space.

Abstract

The predictions of inflation are usually defined in terms of equal time in-in correlation functions in an accelerating cosmological background. These same observables exist for quantum field theory in other spacetimes, including flat space. In this paper, we will explore how the Wilsonian renormalization group (RG) and effective field theory (EFT) apply to these observables in both flat and de Sitter space. Specifically, we show that matching the short- and long-distance calculations requires additional terms localized at the time of the measurement that are not captured by the effective action of the EFT. These additional terms only correct the local and semi-local terms in the EFT correlators. In flat space, we give an explicit demonstration by matching in-in correlators of light scalars interacting with a heavy field with the EFT result. We then show how these additional terms arise generically via exact RG. We also compare these explicit results in flat space with the corresponding theory in de Sitter and show that the local terms typically redshift away. Our results are closely related to momentum space entanglement that arises from tracing over short-wavelength modes.