There are some interesting hep-ph articles on the arXiv today. I will mention two of them – both papers are available on sciencedirect.com owned by Elsevier (so their title pages are almost identical). First, there is the paper
But I want to spend more time with
The principle first postulated in 1993 or 1995 says that Nature wants to choose the values of some parameters in the theory to allow the co-existence of "phases" with the same value of the energy density. In this particular paper, they study the principle in the context of supergravity models that allow the co-existence of supersymmetry-preserving and supersymmetry-breaking Minkowski (zero cosmological constant) vacua.
The supersymmetry-preserving vacua may have demonstrably vanishing (or tiny?) values of the cosmological constant (or the Higgs mass), and the MPP then implies the same virtues for the supersymmetry-breaking vacua (for which the vanishing or smallness otherwise looks like fine-tuning).
It seems to me that they only use the other vacua to explain the properties of our vacuum – while the other degenerate vacua remain "unused in physics". In this sense, if I understood the paper well, they are not proposing a version of my favorite paradigm of the cosmological constant seesaw mechanism. I am still in love with the latter idea, spending some research time with it. Sometime in the future, I may write some update about it – how it effectively deals with the existence of fields that take values in a discrete set and how calculations may be done with such variables.
These authors are linking the small magnitude of the dark energy and the Higgs boson's lightness to the vanishing of some couplings near the Planck scale which also seems to be equivalent to the bounds on the Higgs stability and to the degeneracy of the vacua, and so on. There are some specific computations concerning the gaugino condensates etc.
The tip of an iceberg swimming in the ocean is likely to be close to 0 °C.
Unfortunately, the principles and logic of the new way of looking at these things aren't spelled out too clearly. In particular, I don't understand whether MPP could be compatible with string theory. String theory dictates the value of couplings in all of its effective field theories. But could the stringy ways to calculate them be (approximately or exactly) equivalent to the MPP, the requirement that phases may co-exist? Why would it work in this way? And if this doesn't work exactly in this way, could there be some room for such a new principle adjusting the effective couplings?
Why should the MPP be true in the first place? In the usual reasoning about naturalness, we allow some otherwise unnatural values of couplings if they are able to increase the amount of symmetry of the physical theory. A theory with a larger symmetry is "qualitatively different", so the probability distribution may have a delta-function-like peak at the loci of the parameter space with enhanced symmetry.
But maybe points of the parameter space that allow the "co-existence" (can they really co-exist!?) of two ore several phases are also "qualitatively different", even if there is no obvious enhanced symmetry, so they may be more likely. Is that what we should believe? And if it is, is there a clearer justification for this belief?
The analogy with the phase transitions of solids, liquids, and gases may be highly attractive. Think about water. The temperature \(T\) is a continuous parameter and all values are equally likely. In particular, you might predict that the percentage of water whose temperature is 0 °C (plus minus 0.01 °C) will be tiny.
Except that when ice is melting or water is freezing, it spends some time exactly at 0 °C (or whatever is the relevant melting point) because heat isn't being spent to change \(T\) at this point; instead, heat is being spent to change the percentage of ice vs liquid water in the mixture. So indeed, you find lots of places on Earth where the temperature of water or ice is almost exactly 0 °C.
However, in that case of water, I actually gave you a mechanism which explains why the probability density for \(T\) gets a delta-function-like peak at \(T=0\) °C. Could there be a similar "melting-like" mechanism if we replaced \(T\) by the energy density \(\rho\)? And if there is no such mechanism (and let's admit, it seems hard to gradually change \(\rho\)), isn't it a problem for the MPP? Shouldn't a similar mechanism or "qualitative change" of the dynamics be a condition if we claim that some regions of the parameter space are much more likely than others?
There are many interesting questions and "incomplete answers" I can give you but I would like to hear some complete answers and I am not sure that these answers are included – explicitly or implicitly – in this very interesting paper.