Last Thursday we had a colloquium by Frank Wilczek here at CERN. Frank has made some impressive contributions to such different areas as astrophysics, particle physics and condensed matter physics. He has also provided a lot of beautiful insight into quantum field theory (asymptotic freedom, fractional statistics, color superconductivity). This was a good sign. On the other hand, Frank is also a Nobel-prize winner. This was a bad sign. Nobel-prize winners tend to fill their talks with banal statements written in large font to make a more profound impression. In the end, we observed a fight between good and bad. The latter being the winning side, i'm afraid.
Snide remarks aside, the colloquium had two separate parts. In the first one, Frank was advertising the possibility of phantoms appearing at the LHC. Phantoms refer to light scalar fields that are singlets under the Standard Model gauge group. It is impossible to write renormalizable interactions with the Standard Model fermions (except for the right-handed neutrino), which might be a good reason why we haven't observed such things so far. We can write, however, renormalizable interactions with the Higgs. Therefore the phantom sector could show up once we gain access to the Higgs sector.
Various better or worse motivated theories predict the existence of phantoms. Probably the best motivated phantom is the one especially dear to the speaker: the axion. This was the bridge to the second part of the talk, based on his paper from 2005, where Frank discussed the connection between axions, cosmology and ...the anthropic principle. Yes, Frank is another stray soul that has fallen under the spell of the anthropic principle.
Axions have been proposed to solve the theta-problem in QCD. As a bonus, they proved to be a perfect dark matter candidate. Their present abundance depends on two parameters: the axion scale f where the Peccei-Quinn symmetry is broken and the initial value of the axion field theta_0. The latter is usually expected to be randomly distributed because in the early hot universe no particular value is energetically favoured. With random theta_0 within the observable universe, there is the upper bound f <> 10^12 GeV.
The scenario with a low-scale inflation was the one discussed. Now theta_0 is a parameter randomly chosen by some cosmic accident. One can argue that the resulting probabilistic distribution of dark matter abundance (per log interval) is proportional to the square root of this abundance, favouring large values. Enters the anthropic principle. The observation is that too much dark matter could be dangerous for life. Frank made more precise points about halo formations, black holes, too close star encounters, matter cooling and so on. In short, using the anthropic principle one can cut off the large abundance tail of the probability distribution. One ends up with this plot:
The dotted line is the observed dark matter abundance. The claim is that axions combined with anthropic reasoning perfectly explain dark matter in the universe.
My opinion is that postdictions based on the anthropic principle aren't worth a penny. This kind of results relies mostly on our prejudices concerning the necessary conditions for life to develop. If they prove anything, it is rather limited human imagination (by the way, i once read an SF story about intelligent life formed by fluctuations on a black hole horizon :-) Only impressive, striking and unexpected predictions may count. That's what Weinberg did. That's why some exclaimed "Oh shit, Weinberg got it right". Nobody would ever use a swearword in reaction to the plot above...
For more details, consult the paper. If you are more tolerant to anthropic reasoning, here you can find the video recording.