I'm slowly making my way through The Edge ezine's question of the year. I highly recommend this article. It's the best collection of ideas I've seen since, well, last year's Edge question.
One of the entries I like is Paul Steinhardt's entry, It's a matter of time.
Cosmological fine-tuning is a rather complicated issue. There are a lot of constants in the universe, like the fine-structure constant that governs atomic energy levels, or the gravitational constant that binds galaxies together. These constants differ by many orders of magnitude, and these radical differences account for the difference in strength between gravity, electro-magnetism and nuclear forces. When we ask what the universe would look like if we varied these constants by even a little bit, we find that the modified universe can't support stars and galaxies, let alone people.
The instinctive reaction is to remark that the parameters of the universe have been fine-tuned for human life. However, this turns out to be a rather silly remark. Humans (and stars, and galaxies) are direct functions of the constants of the universe. You might say that we are representations of those constants. Our bodies are made of atoms forged in exploding stars that had no choice but to follow the laws of the universe that are governed by our universal constants. The odds that we find our universe consistent with ourselves are always 1:1.
However, we might still wonder why the constants of the universe occupy the position they do in parameter space. If you pick a car out of a parking lot at random and look at its odometer, you would be fairly surprised to find that the car had only 30 miles on it. It's not in the middle part of the distribution of cars. There are a lot more cars with between 20,000 and 21,000 miles on them than there are cars that have clocked 1 to 100 miles.
Physicists are left wondering why the constants are the way they are. It's not a problem per se, but it is a mystery. Ideally, we'll find that there is really just one fundamental constant in the universe, and that all of the other weird constants are inevitable results of simple natural laws. At present we have no such theory, but we do have some interesting schemes to make this "problem" go away.
If there are multiple universes, at least one for each possible set of constants, then there has to be a universe with constants like our universe has. Alternatively, if the universe is oscillating, the universe might be reborn in each Big Bang cycle with different constants. Eventually, the oscillations will map out all the parameter space, and we'll get a cosmic cycle like the one we're in. All these schemes work like the lottery. Though you might initially be surprised that you have won the lottery, you should not be so surprised when you consider that you've played the lottery billions of times.
Well, Paul Steinhardt has a somewhat more elegant lottery system. Steinhardt has proposed that the universe is much older than we think. That the Big Bang is not the beginning of time, but just one of many that have happened over a trillion years. In each cycle the cosmological constant changes slightly. At first this appears much like the oscillating universe lottery, except that Steinhardt's theory makes predictions! That makes it closer to the ideal theory that has universal constants emerging out of a much simpler theory.
Personally, I think that fine-tuning a bit of a non-problem. It's a good extra-credit question, but it doesn't make much sense to ask about the probability of a universe turning out like our own if there's only one universe. It is unclear to me what probability means in the absence of ensembles or repeated trials.