On the equation-of-motion versus in-in approach in cosmological perturbation theory

TL;DR

This paper proves the equivalence between the equation-of-motion and in-in approaches for computing two-point correlation functions in multi-field inflation, extending their applicability to complex models with strong couplings and correlated initial states.

Contribution

It provides a rigorous proof of equivalence between two main methods in cosmological perturbation theory and extends their use to more complex inflationary models.

Findings

Proved the equivalence between EoM and in-in approaches.

Validated the equivalence with explicit examples.

Extended the methods to models with strong couplings and correlated initial states.

Abstract

In this paper, we study several issues in the linear equation-of-motion (EoM) and in-in approaches of computing the two-point correlation functions in multi-field inflation. We prove the equivalence between this EoM approach and the first-principle in-in formalism. We check this equivalence using several explicit examples, including cases with scale-invariant corrections and scale-dependent features. Motivated by the explicit proof, we show that the usual procedures in these approaches can be extended and applied to some interesting model categories beyond what has been studied in the literature so far. These include the density perturbations with strong couplings and correlated multi-field initial states.