# Schwinger-Keldysh Diagrammatics for Primordial Perturbations

## TL;DR

This paper introduces a diagrammatic method based on Schwinger-Keldysh formalism for calculating primordial perturbations in inflationary cosmology, simplifying complex in-in correlation functions and exploring quantum primordial clocks.

## Contribution

It develops a systematic diagrammatic approach derived from classical Lagrangian, applicable even with derivative couplings, and demonstrates its effectiveness in quasi-single-field inflation models.

## Key findings

- Simplified calculation of in-in correlation functions.
- Explicit computation of bispectrum for heavy scalar fields.
- Identification of observable quantum primordial clock signals.

## Abstract

We present a systematic introduction to the diagrammatic method for practical calculations in inflationary cosmology, based on Schwinger-Keldysh path integral formalism. We show in particular that the diagrammatic rules can be derived directly from a classical Lagrangian even in the presence of derivative couplings. Furthermore, we use quasi-single-field inflation as an example to show how this formalism, combined with the trick of mixed propagator, can significantly simplify the calculation of some in-in correlation functions. The resulting bispectrum includes the lighter scalar case ($m<3H/2$) that has been previously studied, and the heavier scalar case ($m>3H/2$) that has not been explicitly computed for this model. The latter provides a concrete example of quantum primordial standard clocks, in which the clock signals can be observably large.