The quantum theory of scalar fields on the de Sitter expanding universe

TL;DR

This paper develops a new quantum mode framework for free scalar fields in de Sitter space, providing solutions to the Klein-Gordon equation and establishing a complete scalar quantum mechanics with energy basis.

Contribution

It introduces a novel time-evolution picture and energy eigenfunctions for scalar fields in de Sitter space, completing the scalar quantum mechanics framework.

Findings

Derived new quantum modes and wave functions for scalar fields

Established energy basis solutions to the Klein-Gordon equation

Enabled canonical quantization with conserved operators and Green functions

Abstract

New quantum modes of the free scalar field are derived in a special time-evolution picture that may be introduced in moving charts of de Sitter backgrounds. The wave functions of these new modes are solutions of the Klein-Gordon equation and energy eigenfunctions, defining the energy basis. This completes the scalar quantum mechanics where the momentum basis is well-known from long time. In this enlarged framework the quantization of the scalar field can be done in canonical way obtaining the principal conserved one-particle operators and the Green functions.