Firstly, Mark says in #4 and #5 that he is not really interested in the 5d brane theories per se, they are just a device to construct interesting 4d effective theories. But if one is only interested in 4d effective actions, then one is free to make up any 4d action you want. In fact if the 4d EFT is the only thing of interest, then the right way to study them is what EFTheorists have been doing for decades, which is to parameterize all possible theories in the EFT framework (possibly assuming some symmetries, field content, etc), rather than restricting to some special subset of EFTs. The only legitimate reason why an EFTheorist would look at a special subset of 4d EFTs, derived from some 5d action, is because they really care about the underlying 5d microphysical theory.

Secondly, Mark claims in #8 that since he only studies the 4d EFTs, then they are not subject to the same experimental constraints that have been found for the 5d theories. But this seems to be a misunderstanding of what an EFT is. If the underlying 5d theory breaks down at an energy scale of, say M, then the 4d EFT will break down at a scale M at the most (and possibly at a lower scale). For scales less than M, the EFT knows about all the details of the full 5d theory through the coefficients in an infinite expansion of operators. So any constraint that the full theory is subject to, is a constraint the EFT is subject to also. For instance, the chiral Lagrangian of QCD does not tip-toe its way around constraints on QCD – it too is subject to all of them (and works, of course). But breaks down as we go up to the QCD scale. In short, the EFT is subject to all the constraints of the underlying microphysical theory, plus more constraints (from a limited range of validity), not less.

Interesting article (even though it goes right over my head) – thanks!

Mark F. The theories I’m writing about are 4d effective field theories, and so on their own don’t face such constraints. However, the original Galileon, and the ones I’ve discussed, certainly can find their origins in higher dimensional implementations. In that case, the extra dimensions are infinite. So far these theories face their most stringent tests from internal consistency (ghost free conditions, lack of superluminal modes, etc.) and from consistency with solar system constraints (such as the Shapiro time delay) rather than from collider measurements.

To the best of my knowledge there is no connection to f(R) gravity, beyond the fact that both have been invoked as possible explanations for cosmic acceleration.

This does sound interesting, but do these theories have certain restrictions on the size of the extra dimensions and, thus, have the potential to be probed by the LHC? The LHC has ruled out certain extra dimensional theories. Do the theories you’re working on fall under this umbrella?

Also, is there any connection between these theories and f(R) gravity? Thanks!

DGP was not invented to describe cosmic acceleration – but indeed many people have worked on it for that, and it certainly is an interesting question. The work I’m describing above is about 4d effective field theories, not really about modified gravity at all. One can consider the galileons, and other similar fields, as arising from higher dimensional physics, or just use that idea merely as a mathematical tool to discover new interesting 4d field theories. The properties I outlined in the post were unexpected and are, I think, interesting enough to warrant some further study. My interests are precisely in seeing whether they constitute sensible theories, which make sense technically. If the answer is yes, I’ll remain interested; if not, then I’ll shift this part of my research interests elsewhere.

The only problem for GR + CC is that the CC is so small (which is perhaps ameliorated by anthropics anyhow). But I’ll take one aesthetic problem over 10 major physical problems any day. And besides, DGP does not address the smallness of CC problem either. So I don’t quite get the fuss over these bizarre modified gravity models. I think that most of the people who work on them are focussed on making cosmological predictions, while sweeping most of the major fundamental issues under the rug. On the other hand, the people who spend their time focussed on fundamental issues, such as black hole information paradox, quantum gravity, eternal inflation, string theory, loop quantum gravity, Wheeler de Witt equation, holography, duality, gauge theory, etc, have never found DGP or Galileons ever being relevant or useful at all.

attended by the majority (but not all, unfortunately) of people in the world working on these ideas.

What do you mean “unfortunately”?

Imagine if the roof had collapsed. This is why royal families, say, never travel together.