Equivalence Principle in Cosmology

TL;DR

This paper investigates how the Einstein equivalence principle applies in cosmological settings, revealing that local light propagation and Doppler shifts are influenced by the universe's expansion, challenging simplified assumptions.

Contribution

It demonstrates that the optical metric in FLRW spacetime differs from Minkowski, affecting local light propagation and Doppler shift measurements in cosmology.

Findings

Optical metric in FLRW spacetime is not Minkowski.

Local Doppler shifts are influenced by Hubble expansion.

Affine structure of light cones must be treated with care.

Abstract

We analyse the Einstein equivalence principle (EEP) for a Hubble observer in Friedmann-Lemaitre-Robertson-Walker spacetime. We show that the affine structure of light cone in the FLRW spacetime should be treated locally in terms of the optical metric which is not reduced to the Minkowski metric due to the non-uniform parametrization of the local equations of light propagation with the proper time of the observer's clock. The physical consequence of this difference is that the Doppler shift of radio waves measured locally, is affected by the Hubble expansion.