The negative findings of the Large Underground Xenon (LUX) dark matter experiment, which is a 370 kg liquid xenon time-projection chamber that aims to directly detect galactic dark matter and which were published at the international dark matter conference in Sheffield, UK, raises questions about the nature of DM.

Not that my opinion is worth much, but I have been thinking this way about it for some time now. I haven't gotten far enough with my math yet and I have only read the heading of the paper you linked which I'm hoping to read tomorrow, but on a lighter, hypothetical note... how would the Hubble constant itself fit on a scalar field basis? Would it be as simple as a linear relationship to the "z" redshift? I think what I'm asking is does the acceleration of the expansion fit the profile of a scalar field as well?

We may indeed have to modify the theory; one unexplained feature of the standard [itex]\Lambda[/itex]CDM model is the presence of several puzzling coincidences.

The energy density of the cosmological constant is of the same order of magnitude as the density of matter today: [itex]\Omega_M \sim \Omega_\Lambda [/itex], when the DE density parameter is constantly increasing.

The age of universe is equal to Hubble time to within observational error bars: [itex]t_0 = H^{-1}[/itex],

and one that doesn't seem to be commented on very much; when [itex]\Omega_\Lambda [/itex] is 10^{-120}, or smaller, than the quantum expectation of zero point energy, and when the DM and the baryonic matter density parameters could be absolutely anything in GR, why on earth should, (to within observational error bars,)
[itex]\Omega_m + \Omega_{DM} + \Omega_\Lambda = 1[/itex]?

None of these relationships are predicted by GR and if the standard theory is the final word then they are all just extraordinary coincidences.

AFAIK nobody is claiming that the standard theory is "the final word". I would say we don't currently have a good explanation of these relationships; but that doesn't mean we will necessarily have to modify GR. It's simply an open question at this point.

Nevertheless the complete failure to detect DM as some kind of particle, despite the detecting equipment performing excellently and beyond, is significant in a way.
What's the next best candidate that is testable?

I confess I didn't read up on the experiment. How do they test for a particle whose nature they do not know?

What if they're looking for 'red' particles but DM is really 'blue'?

I guess the one thing we know is that they do interact gravitationally. So if they found no presence of gravitational interaction where they could have expected it, they can safely say there can't be any DM there. ?

I'm not sure how this could be done with an Earthbound experiment, because any dark matter "halo" attached to our galaxy would be expected to be homogeneous in our vicinity--i.e., same density everywhere. That would mean it would have no local gravitational effects.

We have essentially tested one type of particle that has been very popular for its many attractive features and not even ruled out the entire parameter space for it. There are many other particle candidates that LUX and others simply do not possess the power to test.

The latest I hearf from MOND was that it does not fit observations very well but that it can be made to ... If you assume the existence of additional unseen matter.

They are basically trying to find limits on how much DM interacts with regular matter. So now we have even weaker limits on how weakly it might interact. As of it nature, who knows so far.

Again, I'm speculating from ignorance, but what I'm assuming is that, if they can very accurately determine how much mass is in a volume, and then determine how much gravitational force/curvature is observed, they would detect zero discrepancy. i.e. all gravitationally-interacting particles are accounted for by known, visible particles.

If you look at plots like this one
(From http://arxiv.org/abs/arXiv:1310.8642)
The WIMP is only one tiny region in the mass vs cross section plane. There are many other candidates remaining and I think this graph is not complete either.

No. You are misinterpreting. This is a graph of candidates and, as I said, the detector was constructed explicitly to look for WIMPs (the brown region). My entire point was that there are many other candidates that would not show up in the detector.

For comparison, the LUX experiment could have detected dark matter with cross section potentially as low as about [itex]10^{-45}[/itex]cm[itex]^2[/itex], in a mass range from roughly 1GeV to 1000GeV. That barely touches the top left of that brown rectangle.