The Scalar Field Kernel in Cosmological Spaces

TL;DR

This paper constructs the quantum evolution kernel for scalar fields in FLRW cosmological spacetimes, revealing the light cone structure and applying it to various specific spacetimes.

Contribution

It provides a method to express the evolution kernel solely in terms of the causal propagator, applicable to free and sourced scalar fields in cosmological backgrounds.

Findings

Kernel expressed in terms of causal propagator

Reveals light cone structure in FLRW spacetimes

Applied to Minkowski, de Sitter, and general FLRW spacetimes

Abstract

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.