Do solar system experiments constrain scalar\u2013tensor gravity?

Valerio Faraoni,Andrea Giusti,Jeremy Côté

doi:10.1140/epjc/s10052-020-7721-4

Abstract

It is now established that, contrary to common belief, (electro-)vacuum Brans–Dicke gravity does not reduce to general relativity (GR) for large values of the Brans–Dicke coupling omega . Since the essence of experimental tests of scalar–tensor gravity consists of providing lower bounds on omega , in light of the misguided assumption of the equivalence between the limit omega rightarrow infty and the GR limit of Brans–Dicke gravity, the parametrized post-Newtonian (PPN) formalism on which these tests are based could be in jeopardy. We show that, in the linearized approximation used by the PPN formalism, the anomaly in the limit to general relativity disappears. However, it survives to second (and higher) order and in strong gravity. In other words, while the weak gravity regime cannot tell apart GR and omega rightarrow infty Brans–Dicke gravity, when higher order terms in the PPN analysis of Brans–Dicke gravity are included, the latter never reduces to the one of GR in this limit. This fact is relevant for experiments aiming to test second order light deflection and Shapiro time delay.

Highlights

IntroductionBrans–Dicke theory, originally introduced in Refs. [19,20,21] to account for Mach’s principle, has been generalized to the wider class of scalar–tensor theories [22,23,24] described by the action (we follow the notation of Ref. [25] and use units in which Newton’s constant G and the speed of light c are unity)
Energy with a very exotic equation of state to explain the cosmic acceleration [12]
The parametrized post-Newtonian (PPN) analysis narrowly escapes the problem of the general relativity (GR) limit arising in the full theory

Summary

Introduction

Brans–Dicke theory, originally introduced in Refs. [19,20,21] to account for Mach’s principle, has been generalized to the wider class of scalar–tensor theories [22,23,24] described by the action (we follow the notation of Ref. [25] and use units in which Newton’s constant G and the speed of light c are unity). We provide an answer: the exact (strong gravity) electrovacuum theory definitely does not reduce to GR as ω → ∞ In this limit, a (canonical, minimally coupled) scalar field survives in the limit of the field equations and acts as a matter source [52,53]. The PPN analysis is limited to the weak field expansion of these field equations and, in this regime, the offending terms disappear from these equations, in which the dominant terms introduced by the scalar degree of freedom φ conform, instead, to the usual PPN analysis This simplification occurs only to first order in the deviations of the metric and Brans–Dicke scalar from the Minkowski background, and are bound to reappear to second order and, in any exact (strong gravity) electrovacuum solution of the theory.

PPN analysis and Brans–Dicke anomaly

Conclusions