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There are objects in our universe beyond our horizon which have apparent velocities greater than light because of the expansion of the universe. We can no longer see them because the light from them can never reach us. Lorentz invariance applies to these objects.

Please cite your reference for such an assertion. I've read of such observations that "seemed" to be superluminal, but none that have been verified as likely factual, and the few (or perhaps couple) of such claims I've read of were never backed up with a theory that could explain such an aberrant (IMO) observation. I was under the impression that the "Lorentz invariance" was only applicable to local observations, so I may be mistaken, but if that is the case, it should not be applicable to long range observations that have several possible variables to explain an observational exception. However, if the postulation that objects permanently out of our observation range due to their distance + superluminal velocity then it is not a reasonable theory as far as practical observations go, at this point in our history, and are not possible for verification (obviously). However, such a belief also is apparently ludicrous from the standpoint that even if an object is traveling faster than light, that does not necessarily make it an unobservable object, regardless of the expansion rate of the universe, unless you're trying to say that the universe is expanding greater than the speed of light. It may take 15+ billion years to reach our neck of the woods, but if that object reflects or emits photons, those photons will eventually make their way here (most likely, depending upon several mundane factors revolving around what is between us).The proceeding is not factually based but extrapolation of my understanding of physics in general, so I may be mistaken on a few points.

Yes, it does. This statement is 100% factually incorrect.

My bad. I should have been more specific in stating that I believe that the mathematics showing this to be the case are faulty regardless of the fact that I do not have the mathematics at my fingertips to prove it wrong. I understand Special Relativity and multiple levels of math, but (and I hate to admit this) I simply have the "gut" feeling that something about this "theory" is fundamentally incorrect. I can't explain it better than that, so I suppose my belief can be dismissed out of hand.

I suppose it's the same feeling I get when physicists claim that neutrinos have no mass.

Please cite your reference for such an assertion.

First, I don't need a reference, because this fact is easily provable from well known facts (like the expansion of the universe, and the uniformity and isotropy of space.) You can follow the argument, which is quite simple, in Steven Weinberg's The First Three Minutes which, while dated, is still quite solid factually.

It is very easy for a layman to follow.

Second, Google "Observable Universe" "Horizon of Observable Universe" or "Cosmological Horizon" and you will have access to thousands of unique references, and even pictures.

Finally, if all that is unconvincing, just have a look here. UCLA is a reputable institution of higher education.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL