What to expect from scalar-tensor space geodesy

TL;DR

This paper uses numerical simulations to study the chameleon scalar-tensor theory's fifth force in Earth's orbit, considering complex geometries and atmospheric models, and assesses its detectability via space geodesy, highlighting challenges and potential solutions.

Contribution

It introduces advanced numerical modeling of the chameleon field with realistic Earth geometries and atmospheric effects, and evaluates the prospects of detecting such forces with space geodesy.

Findings

The fifth force effect is potentially measurable but limited by Earth's mass distribution uncertainties.

Multiple measurements at different altitudes can help resolve degeneracies in detecting the fifth force.

Screening effects create back-reaction on satellites, influencing detectability.

Abstract

Scalar-tensor theories with screening mechanisms come with non-linearities that make it difficult to study setups of complex geometry without resorting to numerical simulations. In this article, we use the $\textit{femtoscope}$ code that we introduced in a previous work in order to compute the fifth force arising in the chameleon model in the Earth orbit. We go beyond published works by introducing a departure from spherical symmetry $\unicode{x2014}$ embodied by a mountain on an otherwise spherical Earth $\unicode{x2014}$ as well as by implementing several atmospheric models, and quantify their combined effect on the chameleon field. Building on the numerical results thus obtained, we address the question of the detectability of a putative chameleon fifth force by means of space geodesy techniques and, for the first time, quantitatively assess the back-reaction created by the screening of a satellite itself. We find that although the fifth force has a supposedly measurable effect on the dynamics of an orbiting spacecraft, the imprecise knowledge of the mass distribution inside the Earth greatly curtails the constraining power of such space missions. Finally, we show how this degeneracy can be lifted when several measurements are performed at different altitudes.