Constraining the attractive fifth force in the general free scalar–tensor gravity with solar system experiments

Xing Zhang; Bo Wang; Rui Niu

doi:10.1140/epjc/s10052-024-12723-8

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 381
https://doi.org/10.1140/epjc/s10052-024-12723-8

Regular Article - Theoretical Physics

Constraining the attractive fifth force in the general free scalar–tensor gravity with solar system experiments

Xing Zhang¹^,2^,3^a, Bo Wang⁴^,5 and Rui Niu⁴^,5

¹ School of Physics, Northwest University, 710127, Xi’an, China
² Shaanxi Key Laboratory for Theoretical Physics Frontiers, 710127, Xi’an, China
³ Peng Huanwu Center for Fundamental Theory, 710127, Xi’an, China
⁴ CAS Key Laboratory for Researches in Galaxies and Cosmology Department of Astronomy, University of Science and Technology of China, Chinese Academy of Sciences, 230026, Hefei, China
⁵ School of Astronomy and Space Sciences, University of Science and Technology of China, 230026, Hefei, China

^a zhxing@nwu.edu.cn

Received: 21 December 2023
Accepted: 26 March 2024
Published online: 9 April 2024

Abstract

In this paper, we focus on the general free scalar–tensor gravity with three free coupling functions, which in the near-field region looks like general relativity (GR) plus a fifth force of Yukawa-type induced by the scalar field. We show that the fifth force is always attractive in the theory. We investigate the effects of the attractive fifth force and calculate in detail the fifth force-induced orbital precession rate $δ ω / ω$ $\delta \omega /\omega$ and the parameterized post-Newtonian parameters $γ$ $\gamma$ and $β$ $\beta$ , all of which depend on the fifth force parameters and the interaction distance. It turns out that, due to the attractive fifth force, $δ ω / ω$ $\delta \omega /\omega$ is always greater than zero, $γ$ $\gamma$ is always less than one, $β$ $\beta$ is greater than one at large distances, and additionally this class of theories is ruled out as an alternative theory to dark matter. We place stringent constraints on the fifth force parameters by combining the lunar laser ranging (LLR), Cassini, and Mercury precession experiments, and derive the upper bounds on the strength ratio of the fifth force to gravitational force at different scales from the LLR observation. We find that the Mercury constraint is not competitive with the LLR and Cassini constraints and the LLR observation imposes much more stringent bounds on the strength ratio on large scales than on small scales. Our results show that this theory is sufficiently close to GR for a small enough fifth force strength and can reduce to GR with a minimally coupled scalar field in the absence of fifth force.

© The Author(s) 2024

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