A Tree Theorem for Inflation

TL;DR

This paper introduces a theorem that simplifies calculating the generating function for tree graphs in the in-in formalism by solving classical equations of motion with constraints, demonstrated through inflationary cosmology.

Contribution

It presents a novel tree theorem linking quantum generating functions to classical equations of motion in inflationary models.

Findings

The generating function can be obtained by solving classical constrained equations.

Application to inflaton field evolution in Robertson-Walker background.

Provides a new computational approach for inflationary perturbations.

Abstract

It is shown that the generating function for tree graphs in the "in-in" formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton field in a Robertson--Walker background.