It's raining today in San Francisco. So I'm inside watching the Michigan State , Kentucky basketball game with my pal Brian. I went to grad school with Brian- he was in the applied math dept. Last night we both decided to celebrate accepting faculty positions. Brian is the Ernest Hemmingway of math, he is quite the reniassance man, and check this-he is taking a faculty position at in Cairo, Egypt!
Friday, I finally mustered the confidence to explain my recent work on the cosmological constant to my colleague Amir-Kashani Poor who is a brilliant string theorist-more on the mathematical side. He recently wrote a very cool paper with Shamit-Kachru on flux compactification in string theory, a very important topic in string theory, of great technical and phenomenological relevance.
So how did I propose to solve the cosmological constant? Remember that in a previous entry, I tried to argue that the cosmological constant is a serious problem that affects microscopic and cosmological scales. It is the sum total of all contributions to the zero point (vacuum fluctuations) energy of all quantum fields. In this sense the vacuum energy influences gravity by causing acceleration of space-time. Observations on the expansion rate today and from the Cosmic Microwave background radiation tell us that the vacuum energy disagrees horribly with the prediction from our current physical theories. So the question to solve is: If the vacuum energy really is huge, why does it not gravitate as Einstein's theory of general relativity predicts? Of course, we could just assume that there is some magical cancellation which renders the cosmological constant small.
My insight was a simple one. I stared at the Einstein equations and realized that the cosmological constant manifests itself in two ways (rather than as a source of energy density with negative pressure, or curvature). This observation was staring at us but no one seemed to stare back and say hi to it. I did. . . It turns out that the CC shows up as a topological 'vacuum angle' in general relativity. Whats a vacuum angle, you might ponder? We are very familiar with vacuum angles in the theory of the strong interactions (QCD). This vacuum angle has no classical effects whatsoever, but since QCD is a quantum theory, it has serious consequences in the quantum domain.
In QCD a non vanishing vacuum angle violates CP (charge and spatial reflection symmetry) But we observe that the strong interactions to a great degree, respects CP from observing a very small electric dipole moment of the neutron-we would not be very healthy if the neutron had a huge electric dipole moment! Well I realized that in general relativity the cosmological constant (here I mean the bare cosmological constant) plays a similar role in violating Parity by manifesting itself as a vacuum angle. Then the solution was simple.
I employed the wisdom from QCD, a dynamical relaxation mechanism that was ingeniously constructed by Roberto Peccei and Helen Quinn (who is a Prof here at SLAC, and who also graciously taught me first hand the mechanism). The idea is straightforward. Peccei and Quinn realized that one can rotate away the vacuum angle interaction my making fermion masses complex. From quantum tunneling effects (Instanton effects) when these fermions get a vacuum expectation value a potential is generated. Now if we make the angle a dynamical field we get a potential which relaxes the vacuum angle to a very small value.
I was able to employ the same idea in gravity. My mechanism was slightly different though. I showed that if there is a massive fermion which ONLY couples to gravity then, if they condense in to a boson (like a Cooper pair) this condensation process generates a potential which relaxes the cosmological constant to nearly zero. Whats really going on physically? Two things.
One reason can be summarized with an analogy with superconductivity, the vacuum state with a huge cosmological constant is unstable-this instability is signalled by an energy gap which seperates this huge cosmological constant state and the small cosmological constant. The size of the gap is the difference in energy. This energy goes into making a condensate between the fermions (their binding energy), in a sense the fermions 'eat up' the would be cosmological constant. This process, naturally (mathematically speaking) relaxes the cosmological constant to the bottom of the potential.
As a result there is a new particle in the game, a condensate, which may possibly be a candidate for dark matter. So whats cool about this way of dealing with the cosmological constant problem is that in solving it we get dark matter out of it naturally (but I still need to calculate this effect-but then again this is a blog so I'm allowed to go off on some speculation)
Well I hope that this helps and that you blogodadaians have some good questions and criticisms for me. After all this is how I make progress.