Can the centers of galaxies act as particle accelerators? At the centers of galaxies, the amount of dark matter is much higher than that of ordinary matter. So the centers can effectively gravitationally attract and accelerate ordinary matter- without much resistance - to much higher speeds than a similar mass of purely ordinary matter would, since ordinary matter interacts very weakly with dark matter. Is this reasoning correct?
If my above reasoning is correct, (and assuming the matter doesn't fall all the way into the super-massive black hole) then can the energy of the particles reach values higher than that in the LHC and other particle accelerators? Can we draw any conclusions about beyond-the-standard-model particle physics by astronomical observations of galactic centers?
 A: Galactic centers can be quite powerful emitters of many RF frequencies from radio waves to IR, visible and UV radiation, to X and gamma rays, if they are active. Active means that they are most likely supermassive black holes (BHs), a million to ten billion or more solar mass BHs,that are accreting huge amounts of mass off a disc spinning g around the BH. They can be the core of Seifert galaxies, as well as the quasars and X Ray and gamma ray sources. 
If a BH is feeding on a disc of material orbiting the BH, they will be radiating huge amounts of energy. The energy has to be released somehow so the rest of the mass can fall into the galactic nucleus. It may have collimated emissions in the axis parallel to the BH rotation. See https://en.m.wikipedia.org/wiki/Active_galactic_nucleus
Cosmic rays detected on earth or near space can be quite powerful also, actually more than the gamma rays because the massive particles can can augment their mass energy with kinetic energy. Cosmic rays are mostly protons, alpha particles, electrons, and some of the light nucleuses. The largest energy cosmic ray detected was 40 million times more energetic than the LHC energy particles, at about tens of millions of TEV. So, yes, there is in fact significant efforts to detect them and their decays and collision debris. 
See UCLA BSM physics combining particle and astroparticle physics at http://www.pa.ucla.edu/content/theory-elementary-particles-astroparticle-physics-and-phenomenology-tepapp
and a popular article about using cosmic and gamma rays also at https://www.forbes.com/sites/startswithabang/2016/11/29/cosmic-rays-may-reveal-new-physics-just-out-of-lhcs-reach/#4b620ae669bf
Edited correction on 2/3/18Due to @Kyle Kanos comment which is correct. Some cosmic rays are believed to come from supernova explosions, and the most energetic ones more than likely from active galactic centers (AGN) which are powered by accretion into supermassive black holes. Since most will also have rotation the magnetic fields and rotation will accelerate the particles. They've been detected at up to energies of about $10^{21}$ ev.
A: In short yes there is some scope for this, but as pointed out by another post the active research on dark matter is generally focused on the edges of galactic disks.
However. Galactic nucleii are likely to be the main source of new fundamental physics. Cosmic rays hit the Earth with -as also previously posted- far higher energies not only than the LHC, but than any particular possible Earth-based particle accelerator, just not predictably and conveniently where we want them. Until now.
LIGO is just the first generation gravitational observatory, and the first collision generated hundreds if not thousands of papers (one paper had 4,000 authors, indicating the scale of this research). A space-based gravity wave observatory already planned will increase the information dramatically. And knowing where black holes and neutron stars are colliding, we can point other detectors there and learn about vastly more energetic events than through the LHC.
One of the things we may be able to do with this, is compare expected and actual transmission of different signals. And get a far clearer more objective map of masses between us and such events, potentially ruling out or in some of the ideas about dark matter. 
In the long run, galactic nucleii will be second only to the Big Bang itself as a place to look for new physics. In various ways, that must include answers relating to dark matter and energy. 
