Somewhere I read that the Hulse-taylor binary pulsar can not differentiate between competing theories assuming different speeds of gravity. Is it mathematically true in general, that the orbital decay of two orbiting bodies cannot possibly favor certain speeds of gravity over others? If so, why is it the case? Any references would be much appreciated!
Edit: I found the page where I read it:
The speed of gravitational radiation ($C_{gw}$) depends upon the specific model of Gravitation that you use. There are quite a few competing models (all consistent with all experiments to date[~1992]) including of course Einstein's but also Brans-Dicke and several families of others. All metric models can support gravitational waves. But not all predict radiation travelling at $C_{gw} = C_{em}$. ($C_{em}$ is the speed of electromagnetic waves.)
So, is it possible to construct a metric theory of gravitation with arbitrarily chosen $C_{gw}$, so that it will be consistent with orbital decay experiments to date? If not, what is the possible range. I believe it must have been discussed in scientific literature, but I can't find anything.
I know that it can be a very hard question to answer with mathematic rigor, but a non-technical overview should be sufficient.
