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.

Comments

[Aaron]

VERY COOL! I didn't understand most of what you said, but am I right to infer that you think you've closed the famous 120-order-of-magnitude gap between predicted and observed vacuum energy? That would be crazy. Good luck!

p.s. I didn't know neutrons were considered dipoles! Is this because of the distance between the oppositely charged up and down quarks, or something else entirely?

[A]

" This process, naturally (mathematically speaking) relaxes the cosmological constant to the bottom of the potential." Good. But what decides the value at this minimum. As I understand it this is the real question.

[stephon]

You've got a main point of my investigation. "What decides the value at this minimumm" In my paper there is a final equation which specifically addresses this point. The equation relates the magnitude of the fermion energy gap to the bare cosmological constant. If in the theory of quantum gravity the ground state has a fermionic energy gap that is the same magnitude as the bare cosmological constant (this is a dynamical statement) then the "decision" is made.

Currently, I am doing this calculation. This is all I can say at the moment.

[Rafael]

Are you doing the calculation by hand or using computers?

[Michael]

Hi Stephon,

Jacques Distler has a very interesting critique of your work:

http://golem.ph.utexas.edu/~distler/blog/archives/000541.html#more

It would be very interesting to hear your response to it!

Best wishes,
Michael

[stephon]

Thanks for pointing this out to me Michael. I read it this morning. I'll respond this weekend, but first have to rederive his technical points.

[Homeboy]

That Distler- whatta a gangsta! Ouch!

[Paul Valletta]

Hi Stephon, great to hear you have a new position. I want to clarify something about what I have been working on, the 'Tale of Two Cosmological Constants', I have not read your paper yet!..but found your blog whilst in CERN pages.

Our Cosmological data is based on Positive Matter, but Negative Matter, or specifically Negative Energy contributes as the value that exists between all 'ordinary' matter, the Negative Vacuum Constant is varying, but the Positive CC is fixed. Some Vacuum Lengths are always being stretched,the further away from ordinary Energy/Matter, the more the 'expanding lengths' occupy space.

What I gather from the above posting, is that you are proposing that strong interactions in and around ordinary matter, are fixed in a finite way by 'using energy made from certain lengths', so the potential is always full of ordinary matter, there is no Anti-Matter whilst there is certain Vacuum States?..yet if we move away, then the potential increase's..and therfore Anti-Matter equates to the Energy Potential, say between Galaxies that are at a far distance from one another.

Interesting, is when one equates the Einstien Field Equations at a far away location, Negative Energy has a Vacuum Solution of expansive energies only?..I s this something that you have considered?

[Paul Valletta]

If I may post this link:

http://www.colorado.edu/physics/2000/bec/evap_cool.html

The 'condensate' may become clear?

[Jack Sarfatti]

I have a very similar theory about the ZPF pressure where the "vacuum angle" is the Goldstone phase of the Higgs field.
Details are in my new book Super Cosmos http://amazon.com
& in Discussion Forum at
http://stardrive.org/title.shtml
Jack Sarfatti PhD Physics (University of Californian degree)

[Jack Sarfatti]

I have a very similar theory about the ZPF pressure where the "vacuum angle" is the Goldstone phase of the Higgs field.
Details are in my new book Super Cosmos http://amazon.com
& in Discussion Forum at
http://stardrive.org/title.shtml
Jack Sarfatti PhD Physics (University of Californian degree)

[kirk edward gaulden]

The electrodynamic fields are used to a cool
hyperspace moment and rips the electrons from the mass to distribute matter through out the region causing a singularity which is a battle between fermions and bosons for
energy distribution, balancing where anti-graviton takes over at the core of the stars in certain singularity and causes the planets hold there position.