Manifestly Unitary Cosmological Perturbation Theory

TL;DR

This paper refines Weinberg's perturbation theory for cosmological calculations, ensuring consistency with standard in-in methods across various spacetime models, thus enabling more efficient and reliable early Universe predictions.

Contribution

It introduces a small adjustment to Weinberg's perturbation series that guarantees agreement with standard in-in calculations for a broad class of cosmological spacetimes.

Findings

Adjusted Weinberg's perturbation series matches standard in-in results

The method applies to various spins and masses in de Sitter spacetime

Generalization to slow roll spacetimes achieved

Abstract

The next decade will feature an abundance of novel cosmological data, while many fundamental questions about inflation remain. Given this, there is ample need for maximally efficient calculations, especially in non-standard scenarios for the early Universe. In inflationary cosmology, observables are computed within the framework of in-in perturbation theory. Weinberg introduced a now-widely used re-organization of perturbation theory for in-in calculations. There is a subtle difference in the $i\epsilon$ prescriptions of Weinberg's perturbation series with traditional in-in, which could interfere with the projection onto the interacting vacuum. In this work, we show that a small adjustment to Weinberg's perturbation series yields agreement with standard in-in at every order of perturbation theory for commonly studied spins and masses in de Sitter spacetime. We then generalize the result to a large class of cosmological spacetimes, including slow roll spacetimes.