Do solar system experiments constrain scalar–tensor gravity?

Abstract

It is now established that, contrary to common belief, (electro-)vacuum Brans-Dicke gravity does not reduce to general relativity for large values of the Brans-Dicke coupling ω. Since the essence of experimental tests of scalar-tensor gravity consists of providing stringent lower bounds on ω, the 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. This fact is relevant for experiments aiming to test second order light deflection and Shapiro time delay.

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

“…It follows from the action that only the first condition is needed to actually get GR+Λ. The second condition by itself guarantees that BD goes to GR in the weak field regime, but not for higher orders in the parametrization of post-Newtonian expansion, see for instance [1020].…”

Cosmology at the top of the α′ tower

“…Note that something similar happens when looking at the Einstein-gravity limit of other modifications to GR that involve a scalar field non-minimally coupled to gravity. For instance, in Brans-Dicke gravity, Einstein gravity with the addition of a massless scalar field is recovered when the trace of the matter energy-momentum tensor vanishes (e.g., as is the case for radiation); see, e.g., [65][66][67].…”

First-order thermodynamics of scalar-tensor cosmology

“…The two sets of exponents with upper or lower sign correspond to the socalled fast and slow solutions, respectively, a nomenclature tied to the behaviour of the Brans-Dicke scalar at early times [11]. This solution is endowed with a Big Bang singularity for t → 0 and its limit for ω → +∞, namely a(t) ∝ t 1/3 and φ = const., does not reproduce the corresponding GR solution, which is Minkowski space (this is a well-known anomaly of the ω → ∞ limit of Brans-Dicke theory [11], which can be approached also with the effective fluid formulation of this theory [27]). The behaviours of the scale factor and the scalar field yield…”