For many years anthropic reasoning had a bad smell in particle physics. It seemed to imply the arrow of causality in the wrong direction – that our existence determines something about fundamental physics. For me, this changed with Weinberg’s discussion of the cosmological constant as an anthropic constraint. This redirected the point of view. If there can be multiple domains in the universe (the so-called multiverse or landscape) then it is natural that we find ourselves in an anthropically compatible domain. Since there is presently no other sensible theory of the cosmological constant, this becomes a strong motivation for the consideration of these types of theories.
I became involved in the subject starting in 1998 through a discussion of the anthropic constraints on the Higgs vacuum expectation value, connected with another of the great fine tuning problems of particle physics. (See also this for a shorter more readable version. ) Here the key constraint is the existence of nuclei and atoms, and the conclusion is that the weak interactions (responsible for quark masses) must overlap with the strong interactions (responsible for most of the mass of protons and neutrons). In recent work with Thibault Damour we have provided yet tighter constraints due to the quark mass dependence in nuclei and in nuclear matter. Our primary constraints are on the quark masses, as nuclear binding is amazingly sensitive to these, but we can also interpret this as a constraint on the Higgs vev if the other parameters of the standard model are held fixed.
While it is nice to know the anthropic constraints – since they provide further motivation for this type of theory – they are not otherwise fundamental. However, since there are many quark and lepton masses (or more generally Yukawa couplings), and these have no obvious pattern aside from a rough generation structure, I have become interested in whether these could tell us about the underlying theory that generates such a landscape. Remarkably these masses look strongly as if they came from a random scale-invariant distribution. In such landscape theories this is quite significant and is possibly the visible remnant of the dynamics of the underlying theory. Andi Ross, Kushik Dutta and I have provide an extensive statistical analysis of the nature and effects of this scale invariant distribution , including quark mixing angles and CP violation. This is a form of phenomenology that one can do in landscape theories even with a single domain.
Andi, Koushik and I have also worked with Max Tegmark, providing some more evidence for this distribution and using it to describe a measure of the likely values for the Higgs vev even in situations where all of the parameters of the standard model vary in a landscape. Our conclusion is that the most likely values of the vev, constrained by the existence of atoms, are in a range somewhat near the observed one. This makes it plausible that the atomic constraints are the solution of the hierarchy problem within landscape-type theories.
Here are also papers describing the connection to of these ideas to the fine-tuning issues of particle physics and to the dynamics of the multiverse.
I am not sure how much longer this line of research will be fruitful.