# Do Solar System experiments constrain scalar-tensor gravity?

## TL;DR

This paper investigates whether solar system experiments can effectively constrain scalar-tensor gravity, revealing that second-order effects are crucial for accurate tests and that linear approximations may overlook important deviations from general relativity.

## Contribution

The study demonstrates that the PPN formalism's linear approximation misses second-order effects, which are essential for testing scalar-tensor theories against experimental data.

## Key findings

- Anomaly in the limit to general relativity disappears at linear order
- Second and higher-order effects reveal deviations from general relativity
- Experimental tests of light deflection and time delay are sensitive to second-order effects

## 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 $\omega$. Since the essence of experimental tests of scalar-tensor gravity consists of providing stringent lower bounds on $\omega$, 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.