Integrating out Heavy Fields in Inflation

TL;DR

This paper develops a method to integrate out heavy quantum fields during inflation, revealing nonlocal, oscillatory effects that are crucial for constructing accurate inflationary potentials and connecting theory with observations.

Contribution

It introduces a novel procedure for integrating out heavy fields in de Sitter space, highlighting nonlocal effects and oscillatory phases that differ from static space-time results.

Findings

Effective interactions are of order H/M.

The resulting effective couplings form a perturbative series in ΔE/M.

Nonlocal, oscillatory effects are essential for inflationary models.

Abstract

I present the procedure for integrating out quantum fields whose mass M is well above the Hubble scale H in de Sitter space. The effective interaction and density matrix are explicitly computed for a simple example and are found to be of order H/M, are nonlocally distributed in time and contain a highly oscillatory phase. This radical departure from the static space-time result demonstrates that these new tools are necessary for constructing effective inflationary potentials. The effective coupling naturally forms a perturbative series in the relative energy transferred \Delta E/M, whose coefficients can then be compared to observation.