Monday, March 25, 2019

Can gravitinos form some Cooper pairs?

The cosmological constant problem is hard. Many people have said it was the deepest problem in physics, especially around 2000 when this proposition was fashionable. But there's no guarantee that its resolution would transform all of physics. The right solution could very well be an idea that is isolated from the rest of fundamental physics.

Why is the cosmological constant positive yet so small? Like $$10^{-122}$$? The most boring solution is the multiverse solution in which our Universe is chosen from a large number, of more than $$10^{122}$$, potential Universes. Life can't form in the Universes with too large or too small values of the constants, so it's unavoidable that from the many choices, people end up here, wondering why the cosmological constant is so small. But it couldn't have been otherwise. This anthropic tautological explanation is unattractive for many of us.

There may be a quintessence, a scalar field that makes the cosmological constant decrease as the Universe gets older. Or there may be some totally new "fake dark energy" linked to holography or MOND or some non-local phenomena in the Universe.

Dark matter seems to be less conceptually game-changing – because it is probably just composed of some "particular localized stuff", like a new particle species (or black holes of some size etc.) – but it's also unknown and its complete independence from the cosmological constant (or, more generally, dark energy) is also questionable.

The CMS Collaboration has recently seen a hint of the gauge-mediated supersymmetry breaking which would mean that the dark matter is composed of gravitinos – and they would be very light, like up to $$1\eV$$. Such gravitinos could even be unstable if the R-parity were broken – but for them to remain dark matter, their lifetime would have to be billions of years.

It's tempting to realize that this most intriguing mass of gravitinos, $$1\eV$$, is also just a bit higher than the neutrino masses and/or the fourth root of the vacuum energy density equivalent to the observed cosmological constant. Couldn't the gravitinos clarify both dark matter and dark energy?

For quite some time, I've been worried – or provoked by the exciting possibility – that we're overlooking some rather rock-solid, established effect whose proper incorporation could actually solve the cosmological constant problem and other problems. A typical example of these possibilities is some overlooked "condensed-matter-like dynamics" involving the new elementary particles.

Imagine that you have gravitinos whose mass is $$1\eV$$. It's some $$10^{-30}$$ Planck masses. The gravitational force between two gravitinos is extremely tiny. Can you create a bound state? A pair of gravitinos that is bound by gravity? Such a bound state would be astronomically huge or super-tiny sub-Planckian geometrically (and very loose). Homework: Calculate the radius.

But maybe it's wrong to assume that the gravitinos only interact through their tiny mass. They also have the angular momentum, $$j=3/2$$, don't they? Well, in this sense, they're not too different from neutrinos with $$j=1/2$$. Isn't there some attraction between two spinning objects? The immediate answer is No, the spinning objects have the gravitational fields like some tiny Kerr black holes. And Kerr black holes make other objects rotate "around" instead of attracting them "radially".

Maybe one should be more careful in trying to solve the two-body problem with the spin-induced "magneto-gravitational" force. And there could be some "more compact" bound state of two gravitinos. Let's call this hypothetical object the gravitino Cooper pairs. Such pairs could get condensed. The bosonic field corresponding to these Cooper pairs could be analogous to the quintessence in some respects. In particular, it could be capable of canceling some fields – ideally the contributions to the vacuum energy density.

If you were really exact, the usual perturbation theory could already break down at all energies greater than the tiny gravitino mass. But the breaking of the perturbation theory could be very limited in effect.

Aside from superconductivity and superfluidity, condensed matter physicists know many more things that can be done with particles. I feel that particle physicists universally assume that most of these are impossible in the vacuum which is why our treatment usually looks like a mechanical QED-like perturbation theory. But what if we overlook something trivial like that? Something that doesn't even have to be new physics per se. It may be just old condensed matter physics applied to some particle species that are known or will be known in a foreseeable future.

I think many people should try to write some texts explaining why they believe that none of these effects may take place – and others should look for loopholes and bugs in these arguments.

A part of the blame for the potential stupidity of this blog post goes to Argus Premium Lager, 5%, half a liter. ;-)