OK, I know that for near objects like Alpha Centauri, we use triangulation to determine how far away they are. I'm kind of confused about the way that we measure further out. I've been given to understand that we use the brightness of objects that we know will always give off the same amount of light. They're called something with the word "candle" in it.
How, if we're using that method to calculate far away distances, could we know if the photon densities predicted by the big bang theory are bearing out?
It seems kind of circular. We claim to know that distant objects are not as bright as they should be (the claim that the expansion of space causes the photon density to be lower the further the light travels), but we only know how far away they are because of that brightness?
Maybe I'm piecing together bits of information without putting them in the proper context, but it still does seem like quite a contradiction.