Quantum theory of redshift in de Sitter expanding universe

TL;DR

This paper develops a quantum framework for understanding redshift in a de Sitter universe, linking quantum photon energies with Hubble's law and deriving new quantum corrections and uncertainty relations.

Contribution

It provides a complete quantum theory of the Maxwell field in de Sitter space, including conserved observables and a quantum interpretation of redshift consistent with Hubble's law.

Findings

Expectation values of photon energies follow Hubble's law

Quantum corrections to observable dispersions are derived

New uncertainty relations for quantum observables are established

Abstract

The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying a special attention to the conserved observables and defining the projection operator selecting the detected momenta it is shown that the expectation values of the energies of the emitted and detected photons comply with the Lema\^ itre rule of Hubble's law. Moreover, the quantum corrections to the dispersions of the principal observables and new uncertainty relations are derived.