Big Crunch vs Big Rip vs Heat Death vs Conformal Cyclic Cosmology... What's the Most Common View? I just saw that Penrose recently published a paper on Conformal Cyclic Cosmology and it made me wonder, what exactly is the consensus view these days? I first heard of Penrose in connection with Orch-OR, which I'm not a fan of, but the new paper made me wonder, what camp is winning at the moment?
Personally, my money is on a Big Rip, but I'm curious what others believe and why.
 A: Consensus in cosmology happens when there is observational data that constrains serious practicioners into a particular corner of model space. It will alwys become looser the less constrained a domain is, and this is why it is unsurprising that people are not that strongly in agreement about the long-term future. 
In terms of popularity I think we have the ordering Heat death > Big crunch > Big rip > CCC. The reason is that when cosmologists allow themselves to extrapolate the consequences of their theories they prefer theories that do not introduce extra complications. One might view this as an application of Occam's razor. Note that predicting odd early phenomena in many ways is more accepted, since it looks like at least in principle one can detect early phenomena.
Assuming the expansion continues like a FLRW universe is the simplest assumption, and given current acceleration that gives endless expansion leading to a heat death state. While there are some people who think collapse has not been entirely ruled out by the data, they seem to be a clear minority. 
Big rip theories are very underconstrained: while you get a big rip if $w<-1$ and current data suggest $w\approx -1$, there is a host of related scenarios that include fields that change and allow the effective $w$ to change - selecting between them is hard since observational data will not constrain them much. So this makes people less keen on them.
CCC goes even further, since it predicts some radical and so far never observed phenomena like charge conservation violation (in order to get rid of all fermions). It is very much an interesting minority idea.
