Hi Dr. Adequate. I know it's a bit presumptuous to respond to a question aimed at someone else with the best part of a thousand words, but this might be of assistance to anyone wanting to get a handle on big crunch/big rip scenarios...
USEFUL INFORMATION ABOUT YOUR UNIVERSE
The fate of the universe (big crunch, big rip etc.) depends on a few key factors and is best described by three simple universe models.
To the best of our knowledge, about 73% of the energy in the universe is contained in the vacuum of empty space. This is often referred to as 'dark energy' and sooner or later you're bound to meet someone at a party with an adenoidal voice who'll talk about it at great length and tell you "they call it that because nobody knows anything about it..."
This may be of some use to fend off such people:
A) THE COSMOLOGICAL CONSTANT:
The higher the energy density of the vacuum energy, the faster the universe will expand. If it's too high it will expand so quickly that structure will not be able to form. This is known as a 'big rip'.
If the energy density is too low, the universe won't be able to expand enough to overcome gravity and it will collapse. This is the 'big crunch' scenario.
So far so good. Now for the tricky bit... the vacuum energy density is known as the cosmological constant and it can have a positive, zero or negative value. The value of the cosmological constant in your universe will be the absolute minimum energy density anything in your universe can ever have.
The reason for this is that empty space isn't empty. The vacuum is made of particle/antiparticle pairs that constantly blink into existence and rapidly annihilate each other. These are called 'virtual particles' by some and 'quantum fluctuations' by more helpful people... but more on quantum fluctuations in a minute.
B) FERMIONS AND BOSONS:
Don't forget everything anyone ever told you about particles, but take comfort from the fact that they only come in two basic varieties.
- FERMIONS are the particles that emit and absorb energy in the form of BOSONS, which once emitted travel freely until they meet another fermion.
- FERMIONS consist of quarks (up, down, strange, charm, top and bottom), and leptons (electrons and neutrinos, muon electrons/neutrinos, tau electrons/neutrinos)
- BOSONS (or more correctly the gauge bosons) come in different varieties for different fundamental forces - Photons (electromagnetism), Gluons (strong nuclear force), W+, W- and Z bosons (weak nuclear force).
There are also meant to be Gravitons (gravitational force) but they're going to be extremely hard to detect and Higgs Bosons which should hopefully be a done deal by the end of the year.
C) THE BASIC COSMOLOGICAL MODELS
- 1) EXPANDING UNIVERSE - POSITIVE COSMOLOGICAL CONSTANT
If a universe has a high enough cosmological constant to overcome gravity, it will continue to expand. The further away from each other objects in such a universe are, the faster they will recede from each other.
Such a universe would have negative spatial curvature, like the surface of a saddle. If you drew a triangle on such a surface, the lines would not be straight but would curve inwards like the surface of a concave lens. The interior angles of such a triangle would add up to less than 180 degrees.
An expanding universe with negative spatial curvature would have a positive cosmological constant, and it would be dominated by bosons.
- 2) SUPERSYMMETRIC UNIVERSE - ZERO COSMOLOGICAL CONSTANT
This is the weird one. A universe with no cosmological constant has no vacuum energy. It would expand, but the rate of expansion would decrease as time went on. In other words, it wouldn't grind to a total halt but after a while you'd be hard pressed to tell.
Such a universe would have no spatial curvature. There would be no quantum fluctuations as there is no vacuum energy. Neither bosons or fermions would dominate, their contributions would balance equally.
- 3) CONTRACTING UNIVERSE - NEGATIVE COSMOLOGICAL CONSTANT
Now we come to the case of positive spatial curvature - indicating a closed and bounded universe.
Picture a triangle drawn on the surface of a sphere. The sides of the triangle would be curved lines instead of straight ones. The interior angles of this triangle would add up to more than 180 degrees.
The cosmological constant in a universe of this kind would have a negative value. This would mean that the further objects were away from each other, the greater an attraction they would exert on one another.
A universe like this would end in a big crunch scenario, and would be dominated by fermions.
D) CONCLUSIONS?
Well, maybe not conclusions but if you've read all that, then it might interest you to know:
- Our universe has a small positive cosmological constant
- Our universe is dominated by bosons - just taking photons alone... if you added up the total of all the other particles in our universe and took that total, it would still only come to roughly a billionth of the amount of photons there are.
Although a very small negative spatial curvature has been measured for our universe (by taking very large scale measurements of it) the result was not concise enough. The margin of error is significant enough that it’s not possible to dismiss a positive curvature scenario... but it's not looking likely.
- To the best of my knowledge (how's that for a disclaimer?) the only viable models that have been constructed for cosmologies with a negative cosmological constant are antimatter dominated universes.