Schrödinger field theory in curved spacetime: In-in formalism and three-point function for the inflationary background

Abstract

We review the Schrödinger picture of field theory in curved spacetime and using this formalism, the power spectrum of massive noninteracting, minimally coupled scalars in a fixed de Sitter background is obtained. To calculate the [Formula: see text]-point function in Schrödinger field theory, the in-in formalism is extended in the Friedmann–Lemaître–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.