probably some of us need to get more familiar with the DeSitter group SO(4,1) the best online introduction I know is a few short paragraphs towards the end of Baez TWF 235 http://www.math.ucr.edu/home/baez/week235.html you have to scroll down about 5/8 of the way. on my printer it is arond page 5 out of 8 pages total. If anyone here wants to teach us about SO(4,1), explain stuff, discuss, ask questions about it, that would be constructive. the point is that most everything in physics is built on MINKOWSKI spacetime which is FLATTEST possible spacetime. It is so flat that it doesnt even expand! It is like what spacetime would be if there were no matter in the universe at all and the gravitational field were zero everywhere. DeSitter space is sort of next-of-kin to Minkowski space in the sense that it is FLATTEST POSSIBLE SPACETIME THAT EXPANDS A LITTLE. It is the flattest, most uniform, most symmetric, most empty, most totally vanilla that spacetime can possibly be, if it is required to have a little bit of cosmological constant Lambda in it making it expand. you just add a tiny bit of dark energy, very evenly distributed, so it doesnt introduce any structure or disturb the symmetry any more than absolutely necessary. I never liked the name Minkowski, it reminds me of a stout lady in a fur coat. I used to live in Westchester, and sometimes in New York. I actually would be very glad if we could get off of Minkowski spacetime and move on to something more interesting. But you always have to have an idea of vanilla. Anyway, SO(4,1) is the symmetries of DeSitter spacetime, just like Lorentz group or Poincaré is the symmetries of Minkowski spacetime.