Analysis of Sun/Moon Gravitational Redshift tests with the STE-QUEST Space Mission

TL;DR

The paper analyzes the potential of the STE-QUEST space mission to test the gravitational redshift in the Sun and Moon fields, providing a detailed theoretical framework including corrections to previous models.

Contribution

It offers a comprehensive derivation of the redshift including non-GR effects and corrects prior formalism errors related to atomic recoil in gravitational redshift tests.

Findings

Derived a complete redshift formula including GR and non-GR terms

Identified and corrected an error in previous models regarding atomic recoil

Provided a framework for high-precision EP violation tests with space-based clocks

Abstract

The STE-QUEST space mission will perform tests of the gravitational redshift in the field of the Sun and the Moon to high precision by frequency comparisons of clocks attached to the ground and separated by intercontinental distances. In the absence of Einstein equivalence principle (EP) violation, the redshift is zero up to small tidal corrections as the Earth is freely falling in the field of the Sun and Moon. Such tests are thus null tests, allowing to bound possible violations of the EP. Here we analyze the Sun/Moon redshift tests using a generic EP violating theoretical framework, with clocks minimally modelled as two-level atoms. We present a complete derivation of the redshift (including both GR and non-GR terms) in a realistic experiment such as the one envisaged for STE-QUEST. We point out and correct an error in previous formalisms linked to the atom's recoil not being properly taken into account.