In response to a Quora question, I wrote the following:
[Jordan-]Brans-Dicke theory is actually not consistent with solar system observations unless its dimensionless coupling constant is given an unreasonably large value.
How come, you might ask? After all, the Schwarzschild solution remains a legitimate solution in Brans-Dicke theory! Well... true, but. Whereas in general relativity, there is only one spherically symmetric, static vacuum solution of the theory, in Brans-Dicke theory, there is a whole family of solutions. And not all of them are consistent with the presence of matter. If you take spherically symmetric solutions in the presence of, say, dust and then reduce the dust density to zero, keeping only the central singularity, the solution you get will not be the Schwarzschild solution.
To be more specific, if we write Brans-Dicke theory in the standard form, with the Lagrangian
$$I=\frac{1}{2\kappa}\int d^4x\left(\phi R-\omega\frac{\partial_\mu\phi\partial^\mu\phi}{\phi}\right),$$
(where $\kappa=8\pi G/c^4$, $R$ is the Ricci tensor and $\phi$ is the scalar field), we find that in the first post-Newtonian approximation, the metric will be given by:
\begin{align}g_{00}&=1-2U+2\beta U^2,\\
g_{ij}&=-(1+2\gamma U)\delta_{ij},\end{align}
where $U$ is the Newtonian potential divided by $c^2$ and the Eddington parameters are given by $\beta=1$, $\gamma=(1+\omega)/(2+\omega)$.
In general relativity, $\gamma=1$. Observations (e.g., radio-metric observations from the Cassini probe presently orbiting Saturn) tell us that $|\gamma -1|<2.3\times 10^{-5}$. This is only possible if $|\omega| > 40,000$. Such a large dimensionless parameter is always considered suspect. Not just that, but if you make $|\omega|$ big enough for the theory to work, its predictions become indistinguishable from the predictions of general relativity... and then, as Leo C. Stein suggests, Occam's razor prevails, as we prefer the simpler of two theories (i.e., the one with a smaller parameter space.)
