Is the Brans-Dicke Vacuum Cosmology Theory Still Relevant?

[jcap]

Has anyone heard of papers describing Brans-Dicke vacuum cosmology solutions?

I'd be interested to know if the following calculations make sense.

I assumed a constant mass density vacuum with equation of state ##p=-\rho##.

I then plugged this equation of state into the Brans-Dicke equations of motion for FRW cosmology and confirmed the existence of a static solution with mass scale ##\phi \sim t##.

Maybe, as Eddington speculated in "The Expanding Universe", the atoms are shrinking (as their energy increases with mass scale ##\phi##) rather than space expanding?

People claim that the Brans-Dicke theory has been ruled out by observation but maybe it hasn’t been ruled out if it applies to the whole universe dominated by vacuum energy?

The apparent cosmological redshift, for example, is then explained by the increased energy scale of absorber atoms relative to earlier emitter atoms rather than photon stretching due to space expansion.

I used the following paper which helpfully gives the generalized Brans-Dicke equations of motion for FRW cosmology (Eqns 7,8,9 with equation of state ##p=-\rho## and scalar field mass ##m=0##) :

https://arxiv.org/abs/gr-qc/0604082v4

 

[PeterDonis]

People claim that the Brans-Dicke theory has been ruled out by observation

Not exactly. What is known is that observation constrains the Brans-Dicke ##\omega## parameter to be very large (IIRC it must be at least ##40,000## the last time I checked the limit; the limit might be even higher now with more accurate observations). With ##\omega## that high BD theory is basically indistinguishable from standard GR.

maybe it hasn’t been ruled out if it applies to the whole universe dominated by vacuum energy?

Again, it's not a matter of being "ruled out", it's that the ##\omega## parameter has to be very high, so the theory's predictions are basically the same as those of standard GR.

I used the following paper

The paper doesn't say anything different from the above. It simply hypothesizes (with no basis in actual evidence) that we might at some point to get evidence for a nonzero value of the parameter they call ##\Omega_\Delta##. They then say that if that were to ever happen, we would have to re-evaluate BD theory in the context of cosmology. However, that's a misstatement: what would actually happen is that we would have to re-evaluate the whole framework of metric theories of gravity, because we would not have any single theory that could explain all the data, since a nonzero value of the paper's ##\Omega_\Delta## parameter would be inconsistent with the current evidence that constrains the BD ##\omega## parameter to be very large, so BD theory would not be a consistent explanation of all the evidence we have any more than standard GR would.

Or, to put it the other way around, all of our current evidence is consistent with the expectation that the paper's ##\Omega_\Delta## parameter is zero, so that's what we expect all future evidence to show. The paper gives no good reason to change that expectation; it just hypothesizes future data inconsistent with that expectation and then works out some consequences of that hypothesis.

 

[jcap]

I must admit that I only used the paper to find out the equations of motion for Brans-Dicke FRW cosmology.

I calculated that if Brans-Dicke theory is applied to the Universe as a whole, assuming its mass density is dominated by vacuum energy, then we get a static Universe with a universal mass scale ##\phi## proportional to cosmic time ##t##. I haven't seen any references to such a simple solution which seems surprising to me. Surely I can't be the first person to think of it?!

Therefore I think that the whole solar system, including its Schwartzschild metric, will simply shrink in a manner inversely proportional to the cosmic time ##t##.

But I presume that one could still use Einstein's theory locally as the Planck length would also shrink at the same rate.

Thus experiments on the solar system would not rule out Brans-Dicke theory for the Universe as a whole. The main experimental consequence would be an apparent cosmological redshift due to the difference in mass scale between absorbing and emitting atoms (the energy of the emitted photon itself does not change with mass scale).

 

[PeterDonis]

I haven't seen any references to such a simple solution which seems surprising to me. Surely I can't be the first person to think of it?!

Have you considered the possibility that you made a mistake?

Therefore I think that the whole solar system, including its Schwartzschild metric, will simply shrink in a manner inversely proportional to the cosmic time tt.

The Schwarzschild metric is not the FRW metric, it's a different solution, so even if your "simple solution" above were correct it would not justify the inference you are making here.

I presume that one could still use Einstein's theory locally as the Planck length would also shrink at the same rate.

I don't see how this inference is justified either.

Thus experiments on the solar system would not rule out Brans-Dicke theory for the Universe as a whole. The main experimental consequence would be an apparent cosmological redshift due to the difference in mass scale between absorbing and emitting atoms (the energy of the emitted photon itself does not change with mass scale).

You're just waving your hands here. You would need to first show how the mass scale affects bound states like atoms--you can't just assume that. You would also have to show how the energy of the emitted photon is independent of the mass scale--you can't just assume that either.

But before you do any of that, you should, as I said above, consider the possibility that you made a mistake.

 

[PeterDonis]

I must admit that I only used the paper to find out the equations of motion for Brans-Dicke FRW cosmology.

Then this discussion is not really about B-D vacuum cosmology but about your personal theory, which is off limits for discussion here.

Thread closed.