I wouldn't go so far as to say “no big bang”, at least not exactly. Maybe the phenomenon we interpret as an event at a fixed point in the past is actually happening “all the time” (it's hard to use our language correctly when talking about the thing which defines <time> and <space> in the first place). What if background radiation doesn't actually come “from the past” but is what is left after black holes squirt some of the stuff that fell into them all over space & time in shreds (traversing the singularity)? Just an idea. Anyway, I'm only waiting for the first object to be found that is “older” than the big bang :)