What does the accelerating expansion of the universe mean about its end? So we know that the expansion of the universe is accelerating.When we thought that the expansion of the universe was slowing down,we predicted that it would reach a plateaux and maybe reverse the expansion.
But with the universe accelerating,what will its fate be?It will keep expanding forever?
 A: The ultimate fate of the universe (and here I'm taling about things on cosmic scales not what happens to stars and galaxies etc.) depends on the equation of state of the material within it.
In cosmology the equation of state is represented by a dimensionless number that is the ratio of the pressure to the (energy) density. i.e.
$$ w = \frac{P}{\rho}$$
and from this it can be shown that
$$ \rho \propto V^{-(1+w)} \propto a^{-3(1+w)},$$
where $a$ is the scale factor.
For ordinary matter (gas, dust etc.) $w \simeq 0$, because the energy density of cold, non-relativistic gas particles just falls with the volume of the universe (i.e. the energy density is very big compared with its pressure). For ultrarelativistic particles (think neutrinos in the early universe) $w \simeq 1/3$, because the energy density falls as $a^{-4}$ (the expansion in 3 dimensions plus the cosmological redshift). For dark energy, the value of $w$ is not known exactly, but it is close to $w \simeq -1$. If $w = -1$ then we have Einstein's "cosmological constant", where the energy density of space does not change as the universe expands. However, this is not the only possibility and there are other idea (e.g. Quintessence fields that predict other values of $w$ that change with time.
The combination of measurements of distant supernovae, cosmic mcrowave background and baryon acoustic oscillations do not yet rule out a cosmological constant. A recent paper by the Planck consortium suggests that $w$ is within a few percent of -1.
It turns out that the case $w<-1$, $w=-1$ and $w>-1$ are quantitatively and qualitatively different in terms of future behaviour of the universe.
(1) If $w<-1$ the acceleration means that the size of the Hubble radius will shrink faster than exponentially, whilst the Hubble "constant" (better called the Hubble parameter) increases. That is the distance at which the apparent expansion reaches the speed of light will get smaller. Eventually (depending on $w$), the horizon shrinks to zero and the universe is torn apart in what is known as the "big rip". The expansion becomes more and more dominant, progressively unbinding smaller and smaller structures - starting with galaxy clusters, then galaies, then the solar system and ultimately even atoms and nuclei. For $w = -1.5$, this would happen in some 20 billion years time and the universe as we know it would end.
(2) If $w=-1$ then the Hubble parameter will decrease and asymptotically attain a constant value equal to $\sqrt{\Omega_{\Lambda}} \simeq \sqrt{2/3}$ of its current value. The Hubble radius decreases exponentially as $\exp(-Ht)$ but there would be no big rip. The universe would expand exponentially forever. Objects like stars and galaxies would remain unaffected by the expansion, as they are now.
(3) If $w>-1$ then dark energy will gradually disappear from the universe - that is its energy density will actually decrease with the scale factor. If $w<-1/3$ however, this still implies continuing accelerated expansion (as $a(t) \propto t^{2/3(1+w)}$) and a shrinking Hubble radius, so again, the universe would continue to expand forever with a Hubble parameter that always gets smaller.
A: This part of Lawrence Krauss' brilliant "A Universe from Nothing" lecture describes the fate of an expanding universe quite well. 
Long story short, because the expansion of the universe is accelerating, in a hundred billion years or so the rate will exceed the speed of light (this doesn't require objects to move through space faster than light, that's impossible - it's the space between galaxies which would be stretching at such a high rate that the distance between galaxies will be increasing faster than the speed of light). At this point, nothing outside our galaxy will be visible because the light simply won't be able to close the distance fast enough.
Note: during the expansion, individual galaxies will be held together by gravity and won't expand internally - like people standing on an expanding carpet. Their feet won't be pulled apart and break their legs because they can hold them together, but separate people will find themselves moving apart from each other.
Krauss quite interestingly points out that any astronomers who evolve on planets orbiting main sequence stars at this point (because there will still be plenty of stars in our galaxy) will never know what the universe is really like and will only ever develop theories of a single galaxy.
A: I believe that the ever expanding universe is the most popular theory as of now. But what is making the universe accelerate? We believe it has to do with Dark Matter and Dark Energy but no conclusive research has been done yet. 
So in general, we just don't know what will be the end fate of the universe because there is too much unknown about what is driving the expansion.
