Scenarios for the
end of the Universe have recently become much more varied, due to some old but neglected ideas being revived and some new ones cooked up. After going over the
conventional wisdom on the Big Crunch, I will describe why it is still a possibility despite recent
measurements indicating a "
flat Universe". (To make one thing clear, these measurements do
not disprove the existence of
curved spacetime. What they mean is that the spatial curvature averages to zero over very large regions.)
The old story of the Crunch
It used to be assumed that only two types of stuff were relevant to the long-term evolution of the Universe, matter (including dark matter) and radiation. These are distinguished by the equation of state, in other words the pressure divided by the energy (or mass) density. For matter this is (to good approximation) zero, for radiation 1/3 (in units where c=1). By conservation of energy, this also tells us how the stuff behaves as the Universe expands: they both get diluted, but radiation dies off quicker (it's redshifted). Currently, the Universe is matter-dominated. Both matter and radiation tend to brake the expansion of the Universe.
The ultimate state of the Universe would be decided by balancing the matter against the expansion. If the matter density is less than a certain number called the critical density, the Universe expands for ever and is called an "open Universe". This also means that it has negative spatial curvature. If the density is more than the critical density, the Universe is "closed", has positive spatial curvature and at some point will stop expanding and begin to contract. Topologically, such a Universe is a four-sphere or hypersphere, with the crossover between expansion and contraction at the "equator".
The Big Crunch is then the hypothetical point (at the "South Pole") at which the scale factor by which all cosmic distances are multiplied goes to zero. As one approaches this point, density and temperature increase without limit. At some point the Universe will become radiation-dominated again, but this will not save it from its fate; in fact the extra pressure (counterintuitively) tends to accelerate the collapse. Soon, I am in trouble because the temperature exceeds the Planck energy, and even a theoretical physicist can't tell you what happens after that. "Maybe the Universe undergoes some sort of phase transition and comes out in a new Big Bang!" I hear you cry. Fine, if you want to speculate on such things, but you'll quickly pass beyond the pale of anything that is scientifically meaningful. On the way there you will be cruelly mugged by the Second Law of Thermodynamics, which points out that the entropy of the Big Crunch is enormously greater than that of the Big Bang, so apart from the brain-fryingly unlikely occurrence of a huge negative fluctuation in entropy there is no way you can connect up the one to the other. The entropy problem effectively ruled out the possibility of a cyclic Universe (until very recently, and it's still very dodgy).
The Big Bang was very smooth, but the Big Crunch would not be. The role of gravity on scales smaller than the size of the Universe is to amplify small variations in density and cause stuff to clump together, forming lumps and voids. If enough stuff clumps together at once, you get gravitational collapse into a black hole. In a contracting Universe, density increases and the intensity and frequency of sound waves (which are nothing but density fluctuations) and gravitational waves also increase: so we can expect more and bigger black holes, which may end up eating most of the matter. Anything that passes the event horizon of a black hole is en route to its own Big Crunch in a finite proper time. Black holes may also merge together to form bigger holes, all the while emitting radiation and increasing the oerall entropy. So, rather than being a nice smooth South Pole, the Crunch would be a violent, writhing mess of black holes and wildly fluctuating spacetime wibbles. The sound of the Big Crunch would indeed differ from that of the Big Bang.
New Crunches
Now on to the recent developments. (Bear in mind, though, that even in the old picture, there would be a Big Crunch even if the total density was even slightly over critical. This has not been ruled out.) With the measurement of the luminosity of distant supernovae, it has become clear that the expansion of the Universe has not been slowing down as expected. In fact, it appears to be accelerating! If this observation is correct, one needs a new form of stuff in the Universe with a negative pressure, which is actually dominating the energy density today. Negative pressure implies that the stuff doesn't get diluted when you increase the volume that it occupies! The simplest possibility is the cosmological constant, which is a possible extra term in the Einstein equation. This has pressure equal to minus the energy density and is physically equivalent to a constant vacuum energy (which may arise from quantum field theory). However this is theoretically unattractive because the value of the constant would have to be incredibly small compared to the energies commonly encountered in particle physics, and would have to be fine-tuned to come to dominate just at the present epoch. If there is a true cosmological constant, the Universe will continue to expand and ever faster and will end up big, empty and cold. No Crunch.
The most general possibility is a scalar field (like the Higgs boson) which evolves (changes its value) gradually over the course of cosmological time. If this happens slowly enough, it mimics the equation of state of vacuum energy, but with a slowly-varying value. One can imagine a ball rolling down a very gentle hill, the height above sea level being the effective value of the cosmological constant. This goes under the name quintessence and can also explain the observations. The idea was popularized by Paul Steinhardt, one of the pioneers of inflation - not surprisingly, since quintessence is essentially the same thing as inflation, except much, much slower (and we don't know how it ends). The advantage of quintessence is that it can explain why the accelerated expansion only started fairly recently. Now, the fate of the Universe depends on what happens to the quintessence field in the far future. If the potential energy is always positive then again the Universe accelerates away forever.
But, it is conceivable that the value of the potential will become negative at some point - analogous to the ball rolling down the beach into the sea. (This of course depends on the overall shape of the potential energy.) Then, the Universe is doomed to recollapse into a Big Crunch. Andrei Linde and collaborators have recently emphasized such a possibility and shown that it can come out of some simple (but somewhat unrealistic) supergravity models. See http://arxiv.org/abs/astro-ph/0301087.
. ---------- .0 <- Now : slowly rolling
. .
. .
. .o <- Soon
/ \
/ \
/ \o <- Later
w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^w^
\
\o <- Doomed to collapse!
Horizontal axis: value of
Q (quintessence field). Vertical axis: potential energy. The "waves" mark zero.
Despite the apparent flatness of the Universe and the current accelerated expansion, it is not ruled out that some time in the future (it may be as soon as ten billion years from now!) there will be a Big Crunch. However I have to admit that the theories that allow for one look, at the moment, fairly contrived.