How will the Universe end?  And when? It's been speculation in religion and philosophy since man realized he was special.  Can physics offer anything new?

Let's go to the Dark Energy hypotheses and see.  1998 really messed us up, theoretically. Until then, we knew the Universe had to slow down - well, theoretically.  But then the Hubble showed us truly distant supernovae and we got the uncomfortable reality that the Universe was actually expanding more slowly in the past than it is now.  That meant gravity has not been slowing Universal expansion, it has been accelerating. 

What could cause that?  No one knew but theorists were on the case and all of the explanations (Einstein's cosmological constant, ether, Einstein's theory of gravity is wrong) became a blanket dark energy hypothesis. 

It also meant we don't even know what we don't know.  Dark energy (unknown) became 70% of existence, dark matter (unknown) another 25% and what we know as matter is about 5%.  Sounds like matter doesn't matter, right?  Maybe, though it is actually kind of cool to have space be special.  For instance, matter can't travel fast than light, not even in Italy, but space can.  That explains how the age of the Universe and the size of the Universe are not correlated - if you're limited to light years.

Rate of expansion since the birth of the universe 15 billion years ago. The more shallow the curve, the faster the rate of expansion. At about 7.5 billion years ago, objects in the universe legally  separated and did it fast.  Why?  I don't know.  Trust issues, or maybe they met a younger universe.  Or dark energy. Credit: Ann Feild (STScI)

So there are lots more questions now but that big one has remained constant and no one in the history of human introspection has gotten close; namely, when and how will it end?

The Big Rip is one hypothetical possibility for our Cosmic Doomsday, proposed by a group at the the Institute of Theoretical Physics at the Chinese Academy of Sciences. Dark energy has given them the means to end the Universe the same way a Hot Big Bang and inflation began it.

There's a tiny bit of equation-ing in this piece but I will leave the nuts and bolts ("divergence-free parametrization for dark energy w(z)=w0+wa[ln(2+z)/(1-z)-ln2]") to those who want to read their article (citation below - it's free to read).  You have to essentially accept the equation-of-state parameter w, the ratio of pressure and density of dark energy, and if w<-1 then dark energy density will grow to infinity in finite time (you like that one??) and gravitational repulsion will tear us all to smithereens. 

Well, the Norse missed Ragnarok in 2010, Christianity did not get us last year and our cosmological Nibiru destruction has already passed.  Mayan calendars are looking shaky too.  What do Chinese theoretical physicists say? 

These guys pants the Teutonic pretensions of Chevallier-Polarski-Linder parameterization because w will diverge when the redshift parameter approaches -1 and opt for the Asian divergence-free Ma-Zhang parameterization to foretell the Apocalypse.  After doing a Monte Carlo analysis (spare me - of you read this far there is no point in noting the flaws of doing a Monte Carlo) they came up with a
95.4% confidence level of having the Big Rip at...16.7 billion years.

What does that all mean? 16 billion years is a lot of time so it feels pretty safe. But it's nice to have a number and if they are wrong, no one will be able to tell them.

Citation: LI XiaoDong, WANG Shuang, HUANG QingGuo, ZHANG Xin4, LI Miao, 'Dark energy and fate of the Universe', Sci China-Phys Mech Astron, 2012, 55(7): 1330-1334 DOI: 10.1007/s11433-012-4748-z