Stephon Alexander

Cosmological Constant II

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.

Michael Peskin: The Guru

Hmmm. . . where do I begin. I promised you blogodadians that I would reveal my attempt at giving some insight into the cosmological constant problem yesterday. I swear I wasn't being a sloth. You see the typical occured-I gave the head of the SLAC theory group, Michael Peskin a draft of the paper-or rather he requested it from me. The paper had already gone through the hands previously by two other world renowed, anal retentive, theorists and they both were happy with what I wrote. I have to admit that as much as I have been dying to complete this 3 year long project (It's been on my mind for that long, actively), I was relieved to know that this week Michael would be wearing four hats; rather than the usual 3. This week he is one of the organizers for the International Linear Collider Workshop and he was preparing a talk and heading the group and teaching QFT and .... So this meant that he wouldn't have time to COMPLETELY DESTROY my paper. NOT!

You see, the last project Michael, Shahin (a string theorist that Lenny recruited from Iran; who is also reputed in the community for being a hardcore calculator, was pulvarized by Michael's 'ammunition') and I indulged in, lasted a whopping 11 months, 8 of which had to do with Michael being "confused", trying to unconfuse him took 8 months-deep down Shahin and I thought that he knew the answer all along and just wanted us to walk the path less travelled. . . We worked on a new way to resolve the matter-antimatter asymmetry in the universe. It turned out that Michael's confusion, a phase problem, led to the resolution of the project!

I walked in Wednesday morning and Michael was doing his usual morning pitter patter at his computer-the Kat types fast. I thought "perfect opporunity to just TELL him that I'm putting the paper out today"

"Michael" I said, "You know, I just got feedback from such and such and such and such and they told me that I should post the paper-isn't that great?!"

He replied, "Thats good. . . But you know my life has been insane with the workshop . . . give me 24 hours to go over what you've done"

I sunk is despair, for I feared the worst; Michael was going to obliterate my paper! Everyone in the field knows about the reputation of the SLAC theory group-we are the toughest place to give a theory seminar in the world.
I've heard stories of the infamous seemingly harmless gesture of this nice fella in the audience, with his low keyed voice, raising his hands like a good school boy, "excuse me, but I'm confused." Then a question/statement would splurge out. Meanwhile, I'm saying to myself 'man I wouldn't want to be in the speakers shoe right now'

I recall time and time again the aftermath of that statement-It usually, from a half full glass perspective, would destroy the speakers whole talk (10 minutes into it)-or at least completely clarified the fancy jargon. Those who are experienced at giving seminars at SLAC, try their best to come prepared. The first timers will never ever forget it when the man with the musthache and glasses asks "excuse me, but I'm confused." No, he's not confused any more than Einstein was having difficulties with Math.

Well I had to deal with this for the past three years. Every idea I had, calculation I did was completely deconstructed when it encountered Michael. I welcomed it deep down, because I hoped that just a little
of Michael's virtues would rub off on me.

I met Michael 6 years ago when I was a graduate student. There was this summer school (supposed to be this elite thang) for string theory graduate students called TASI. Anyway, Michael was lecturing. And all I could remember was this guy with a cast on his hand writing on the blackboard with a level of detail and enthusiasm that I'd never seen before. He immediately commanded my respect as the dude that knew everything. I mean, Strings, Supersymmetry, Condensed Matter, Coding, QCD. Man I was scared to talk to him! I finally figured out a way to talk to Michael without him figuring out that I didn't belong at TASI, yeah back then I KNEW that I was the dumbest kid there (and apparently so did everyone else). So I went to him and asked him to suggest a place where I could brush up my SUSY calculational skills. Then he surprised me...

"Come here, lets go up to the computer room" For a whole half an hour, Michael walked me through all the choices on the the ArXiv for learning SUSY. Then he continued to go into more details about the strengths and weaknesses about the final five lecture notes on the web.

So while I sound like 'damn, gotta deal with Michael' it was my dream come true to be in an office next to him for these three years.

But I finally, after three years, asked Michael a question that he didn't have an answer to then I said to him "finally, something you didn't know"

He smiled back.

Out of the Cave

I know... Where the heck have I been? Well, I took a week off and away from anything having to do with physics to reflect on accepting a faculty position. I'm not going to say where it is, but I'm happy to say that I accepted a position. Then there was all of the running around I had to do that I didn't do while I was travelling around for the last four months non stop (such as paying bills and such)

But I still managed to finish up my three year long project on the cosmological constant problem. This problem is reputed as being the 'biggest embarassment in physics' It has haunted all of the greats and all of the insignificants such as Einstein and yours truly respectively. What is the cosmological constant problem? Well my friend Sean Carroll wrote a great piece on the cosmological constant problem. Just do a Google search on Sean (Sean Carrroll Cosmological Constant).

But if you have little patience, let me say a few words. The cosmological constant problem can be understood best from Einstein's theory of general relativity. Schematically(very much so) the theory
states Geometry = Matter & Energy , or in other words space-time curvature/gravity is dynamically
related to matter and energy. The theory is able to make this mathematical relationship concrete with the help of some powerful insights from a branch of mathematics called Differential Geometry; which allowed Einstein to make this relationship independent on the choice of space-time points(or frame of reference)-this is known as the principle of General Covariance.

Now, Einstein realized that he could freely add a constant (hence the name cosmological constant) without violating any of these principles in his theory. Moreover you're free to put it on either side of the equation, but the constant carries different meanings depending on if its on the matter energy side of the geometry side.

Here is where the trouble begins. We once thought that the cosmological constant was zero, now we actually measure a non zero value (exculding the issue if its really a time dependent component of dark energy), the value is extremely small (the energy density is 10^{-33} electron volts^{4}). The problem is that everything in our universe has 'quantum fluctuation' whose zero point fluctuation contributes to the cosmological constant. If we use quantum field theory to the same level of accuracy that we confirm at accelerators, we find a disgraceful disagreement between theoretical and the observed value of the cosmological-how bad? 10^{120} orders of magnitude- It takes longer that the lifetime of the universe to count this number! (which crazy fool would want to do this?)

So what happened to this large cosmological constant?

Or did we get it all wrong? If we did, which theory should we throw out, general relativity or the Standard Model? Clearly we shouldn't throw out either( otherwise get rid of GPS or your cell phone). Some people, like my colleague and guru Lenny Susskind (the inventor of string theory) and Steve Weinberg (co inventor of the Standard Model of particle interactions) state one possible solution is that the cosmological constant is anthropically selected.
Now, these cats are genuises (I mean it!) and they may be correct. But in the meantime it does not hurt to seek a 'dynamical' way to explain that the cosmological constant does not gravitate the way that
the Einstein equations dictate. In other words perhaps there is a way that the quantum theory of gravity deals with a huge cosmological constant. This is what I've been thinking about for the past three years. Now I'm out of the cave with an answer.

Whats the answer?

I'll tell ya tomorrow.