Do solar system experiments constrain scalar–tensor gravity?
Valerio Faraoni, Jeremy Côté, Andrea Giusti
Abstract
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 $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math> . Since the essence of experimental tests of scalar–tensor gravity consists of providing lower bounds on $$\omega $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ω</mml:mi></mml:math> , in light of the misguided assumption of the equivalence between the limit $$\omega \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ω</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math> 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 $$\omega \rightarrow \infty $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ω</mml:mi><mml:mo>→</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:math> 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.