New Spherical Scalar Modes on the de Sitter Expanding Universe

TL;DR

This paper introduces new spherical scalar modes on the de Sitter expanding universe, derived as eigenfunctions of a conserved operator, with computed transition coefficients to other mode bases, advancing understanding of quantum fields in curved spacetime.

Contribution

It presents novel spherical scalar modes on de Sitter spacetime and computes their transition coefficients to existing mode bases, using a specialized time evolution technique.

Findings

New spherical scalar modes are derived as eigenfunctions.

Transition coefficients between modes are explicitly calculated.

The method enhances understanding of quantum field behavior in de Sitter space.

Abstract

New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time evolution picture technique specially developed for spatially flat FLRW charts. Transition coefficients are computed between these modes and the rest of the scalar spherical and plane wave modes, either momentum or energy eigenfunctions on the spatially flat FLRW chart.