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

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.

24 pages, published version

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• Higgs as heavy-lifted physics during inflation
• Comparing multi-field primordial feature models with the Planck data
• Hybrid Quasi-Single Field Inflation
• A Bump in the Blue Axion Isocurvature Spectrum
• The cosmological collider in $R^2$ inflation
• Tree-level correlations in the strong field regime