The \delta N formula is the dynamical renormalization group

TL;DR

This paper derives a systematic method for calculating the inflationary bispectrum using the separate universe approach, incorporating quantum effects and slow-roll corrections, with broad applications in inflationary cosmology.

Contribution

It provides a field-theory based derivation of the separate universe method for the bispectrum, including quantum effects and slow-roll corrections, enhancing the theoretical toolkit.

Findings

Correct matching between quantum and classical parts established

Leading slow-roll corrections to the three-point function derived

Method applicable to complex inflationary scenarios

Abstract

We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.