bcrowell said:
A search for his name on arxiv,
http://arxiv.org/find/astro-ph/1/au:+Bell_M/0/1/0/all/0/1 , gives 31 results. Does one of these papers contain the claim that "if you assume quasars redshifts are cosmological, the resulting explanations are complex and leave many unsolved puzzles?"
If you ignore the hits on "M.E.Bell" and "M.R.Bell" and just stick to "M.B.Bell" I think you'll find that just about every entry in that list relates to such ideas, although that was not a literal quote.
In one I've recently looked at, even the title supports it: arXiv:0812.3130v1 "The Peculiar Shape of the \beta_{ app} − z Distribution Seen in Radio Loud AGN Jets Is Explained Simply and Naturally In the Local Quasar Model". This paper considers why "superluminal" blobs (conventionally attributed to beaming effects) cut off in a strange way for quasars with smaller redshift.
There are also questions of why the density of lines at various redshifts in quasar redshifts is so weakly related to the overall redshift. This is just one of the characteristics that is conventionally partly explained by the "evolutionary" concept that quasars of different ages have different characteristics.
There are also the obvious questions of quasar distribution in space; there is a surprisingly spherical hole around us if we assume cosmological distances. Again, this is conventionally covered by an evolutionary model which says that quasars suddenly stopped existing everywhere at some relatively recent time.
Another aspect is the Arp's original observation that many quasars appear to be have been emitted, often in pairs, by large galaxies of much lower redshift, including most of the brighest quasars. As we only have one sky, it's difficult to evaluate the probability of this occurring by chance, but it certainly looks interesting.
I frequently hear statements that the idea of local quasars has been ruled out by the fact that some of them are surrounded by galaxies at the same redshift. However, this has always been consistent with Arp's original observation, which is that quasars closest to the host galaxy have high intrinsic redshifts and a point-like appearance, or unresolved nebulosity, but quasars further away have much smaller intrinsic redshifts and appear more like galaxies with active nuclei. Also, even if the surrounding material did appear to be a galaxy at the same redshift, this could still be just a matter of some unexplained intrinsic redshift of both the quasar and its surrounding galaxy; if it is possible to have intrinsic redshift in violation of what we expect from GR, we cannot use GR to rule it out at the galactic scale.
There are many other more technical complexities, for example relating to the "metallicity" shown in the spectrum failing to correlate with the evolutionary time scale, and "fingers of God" effects in the supposed spatial distribution.
Another very controversial observation is that the relative redshifts between quasars related to a given host galaxy seems to follow a specific approximate pattern. This might be explained for example by the idea that ejection speeds are relatively low (otherwise Doppler effects would hide this pattern) but ejections occur at regular intervals and the intrinsic redshifts decay in a curiously regular way. The official view is that this must be some form of selection effect in the way the observations are collected or processed, but such effects seem to be surprisingly common.
Explaining intrinsic redshift is very difficult, and current attempts are far too speculative to discuss here. However, on the other side, the cosmological distance view of quasars has been presenting a whole series of weird effects ever since they were discovered, and although we have come up with some sort of possible explanation for each one the problems keep coming.
