Schr\"odinger field theory in curved spacetime: In-In formalism and three-point function for inflationary background

TL;DR

This paper reviews the Schr"odinger picture of field theory in curved spacetime, extending the in-in formalism to FLRW universes, and computes the three-point function for inflationary scalar fluctuations, confirming consistency with Heisenberg picture results.

Contribution

It introduces the Schr"odinger formalism for in-in calculations in curved spacetime and applies it to derive the three-point function in inflationary cosmology.

Findings

Power spectrum of massive scalars in de Sitter obtained.

Three-point function in inflation matches Heisenberg picture results.

Extended in-in formalism applicable to FLRW universe.

Abstract

We review the Schr\"odinger picture of field theory in curved spacetime and using this formalism, the power spectrum of massive non-interacting, minimally coupled scalars in a fixed de Sitter background is obtained. To calculate the N-point function in Schr\"odinger field theory, the "in-in" formalism is extended in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. We compute the three-point function for primordial scalar field fluctuation in the single field inflation by this in-in formalism. The results are the same as the three-point function in the Heisenberg picture.