All-Loop Renormalization and the Phase of the de Sitter Wavefunction

TL;DR

This paper demonstrates that the imaginary part of the de Sitter wavefunction, crucial for cosmological observables, is determined by renormalization scale dependence at all loop orders, revealing deep relations among correlators.

Contribution

It establishes a universal relation for the wavefunction's imaginary part in de Sitter space, valid at all loop orders, based on fundamental principles like unitarity and locality.

Findings

Imaginary part of wavefunction fixed by renormalization scale dependence

Infinite relations among correlators of massless fields and conjugate momenta

One-loop exemplification of the derived relations

Abstract

Cosmological observables of the primordial universe are encoded in the late-time field-theoretic wavefunction. For shift-symmetric scalars in de Sitter, a good approximation for many inflationary models, the wavefunction must be purely real at tree-level. This property is violated by a quantum anomaly in the process of renormalization. As a result, we show that the imaginary part of the wavefunction is fixed by its dependence on the renormalization scale to all loop orders in perturbation theory. This follows from unitarity, locality, dilation isometry and a Bunch-Davies state. The compact relation we uncover for the wavefunction implies an infinite set of relations among correlators of massless fields and their conjugate momenta, which we exemplify at one-loop order.