Yup, the best model indicates endless, accelerating expansion. How we know comes from a combination of theory and observations, which I'll briefly review.

The expansion of the universe is governed by general relativity, which describes how the contents of the universe affect the expansion rate, and the spatial curvature.

The three big ingredients are matter, pressure, and a cosmological constant (AKA "dark energy"). "Dark matter" could be considered a fourth, but its effect is the same as regular matter so we don't bother distinguishing it for this purpose.A higher density of matter causes the expansion rate to slow down, much like gravity slowing down a stone that was thrown upward. If the stone was not thrown fast enough, gravity wins and pulls it back. If a universe is filled with only matter, then following the Big Bang the expansion rate will decrease. If the matter density is high enough, then its gravitational field will slow the expansion to a halt and then pull the universe back together in a "Big Crunch".

Counter-intuitively, pressure (such as that produced by radiation and relativistic particles)

*also* acts to slow the expansion rate. This is because the universe has no edges to push against. So instead of "pushing outward", the momentum of the particles providing the pressure acts as an additional source of gravitation, which is described through the stress-energy-momenta tensor. It also turns out that the effect of pressure decreases more quickly as the universe expands than does the effect of matter, and so it was most important in the early universe (the "radiation dominated era"), and is virtually negligible today.

Finally, there is dark energy, which can be thought of as a negative pressure that remains constant even as the universe expands. Negative pressure acts like an antigravity (more accurately it is best described as an intrinsic property of the space-time itself) and it makes the universe expand faster. This is pretty odd, but it is the most successful model for cosmology that we have (along with dark matter, forming the so-called "Lambda-CDM model", where lambda stands for dark energy and CDM stands for cold dark matter.) Dark energy also becomes more important over time, because its density remains constant while the density of matter decreases. So the universe proceeds from radiation dominated --> matter dominated --> dark energy dominated.

General relativity says that because the expansion of the universe is governed only by the density of these constituents, the fate of the universe is also intimately tied to them. "Density is destiny".

So to find out what model best describes the universe and its fate, we use observations to constrain what these densities are (relative to some "critical density" which would make the universe spatially flat), and check the expansion history. There are three independent techniques that help us do this:

-Type Ia Supernovae, which act as standard candles and give us a measure of the expansion history.

-Cosmic Microwave Background (CMB), for which the angular size of the fluctuations reveal a lot about the universe's contents.

-Galactic Clusters, which constrain the matter density (both regular and dark).

Plotting these data together, here is what we find. Ω

_{M}* *is the density of matter, and Ω

_{Λ} is the density of dark energy, in units of the critical density (Ω

_{M} + Ω

_{Λ} = 1)

The intersection of data show that the universe is

*very* close to the critical density (which makes the geometry flat, such that parallel lines remain parallel and sum of angles in a triangle is 180°). About 30% of this density is in the form of matter, of which only 5% is accounted for by "regular" baryonic matter, and 25% is "dark matter". The remaining 70% is dark energy.

With the dark energy, the expansion is destined to continue forever, accelerating as it does (eventually it becomes an exponential as the universe is dark energy dominated). We can unambiguously reject the Big Crunch hypothesis, unless some dramatic new physics comes into play. Instead we (not really

*we*, but our very distant descendants) are faced with "heat death" as the universe expands, entropy increases, and all structures eventually evaporate into radiation.

There is an open question regarding whether the expansion rate could increase so rapidly that all structures end getting torn apart -- this is the notorious "Big Rip" scenario. Whether or not the Big Rip occurs depends on what we call the "equation of state" of dark energy, characterized by a parameter "w". The Big Rip occurs if and only if w is less than -1, and the further below -1 it is, the sooner it happens.

For reasons of physics, the simplest model would have w be identical to -1, in which the Big Rip takes place infinitely far in the future. This is the boundary case between it occurring and never occurring.

Available data have this to say:

The intersection is consistent with w = -1, so we do not

*expect* a Big Rip, but we also cannot rule it out. The best we can do is constrain how early it could happen, or by how much it can never happen, if that makes any sense.

-edited to fix some sloppy writing.