Understanding the Cosmological Constant Problem

[alexsok]

I do realize that this is an enormous problem in science today (string theory included), but after reading some related material, i have a question i'd like you guys, if possible, to answer...

There are two problems with the cc:
Why is it so small and why is the cc the same order of magnitude as other components of the cosmic energy density today? how did it came to be the non-zero value we see today (cosmic coincedence)? why is it zero at the minimum potential?

Could it be that dynamics favors small cc? even if it isn't a minimum of the potential? That is, could the universe stall at or near cc=0 (minimum potential at cc=0?) and start evolving from there? when u get to zero curvature, the scalar field will seize evolving...

Clearly, that would require some unconventional dynamics, but perhaps that is what cc is telling us...

Perchance, a scalar field controls the dynamics (assuming Vmin<0, minimum is at negative energy: somehow the potential could drift from negative to positive, otherwise the idea would be obsolete).

Let's assume inflation has occured; presumably, large initial CC... the key to this model is NOT special potential, but special form for kinetic term (it could always absorb the cc) and the value of this potential controls the vacuum energy.

Why do u think guys?

 

[marcus]

positive CC plays a role in loop gravity theory

Lambda was generally assumed to be zero prior to 1998 (supernova observations) and the prevailing estimate now is about 0.6 joule per cubic km, expressed as an energy density.

Positive Lambda plays a role both at microscopic scale and macroscopic (cosmological) scale in Loop Gravity

See the recent paper by Girelli and Livine
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

And positive Lambda cropped up in LQG some time prior
to 1998. See for example Major and Smolin 1995 article
"Quantum Deformation of Quantum Gravity"
http://arxiv.org/gr-qc/9512020

Already in 1995 Major and Smolin observed that the constant
played a role both at microscopic and macroscopic scale. It seems
to be required for some versions of the theory and so in a
vague sense Lambda being a small positive constant was "anticipated",
if not definitely predicted, by the theory, prior to 1998.

So far I do not know of any physical theory that predicts a VALUE of Lambda. For instance in a string context it can, so I am informed, as easily be negative as positive and there is no handle on the magnitude.

Two interesting recent papers:
Noui and Roche "Cosmological Deformation of Lorentzian Spin Foam Models"
http://arxiv.org/gr-qc/0211109

Ichiro Oda "A Relation Between Topological Quantum Field Theory and the Kodama State"
http://arxiv.org/hep-th/0311149
Oda's paper came out last month and has a significant final sentence (at the end of the Conclusions section) on page 7:
"Of course, one of the big problems in future is to clarify whether the Lorentzian Kodama state is normalizable under an appropriate inner product or not."

Several months earlier Edward Witten had written that the state was not normalizable under the inner product which he (Witten) apparently considered appropriate and Oda seems to suggest here that this was inconclusive---the problem is still open. Some version of the Kodama state seems to be intermingled with the cosmological constant in these discussions and there seem to be some riddles involved here that interest good minds.

Perhaps answers to some of your questions could come out of this eventually. If the CC plays key roles at both large and small scale in quantum gravity (loop theory and spin foam models both) then the theory may eventually get a grip on it. Lambda is basically a GR thing, so successfully quantizing GR should give some handle on it, one would imagine.

 

[alexsok]

Originally posted by marcus
Lambda was generally assumed to be zero prior to 1998 (supernova observations) and the prevailing estimate now is about 0.6 joule per cubic km, expressed as an energy density.

Positive Lambda plays a role both at microscopic scale and macroscopic (cosmological) scale in Loop Gravity

See the recent paper by Girelli and Livine
"Quantizing speeds with the cosmological constant"
http://arxiv.org/gr-qc/0311032

And positive Lambda cropped up in LQG some time prior
to 1998. See for example Major and Smolin 1995 article
"Quantum Deformation of Quantum Gravity"
http://arxiv.org/gr-qc/9512020

Already in 1995 Major and Smolin observed that the constant
played a role both at microscopic and macroscopic scale. It seems
to be required for some versions of the theory and so in a
vague sense Lambda being a small positive constant was "anticipated",
if not definitely predicted, by the theory, prior to 1998.

So far I do not know of any physical theory that predicts a VALUE of Lambda. For instance in a string context it can, so I am informed, as easily be negative as positive and there is no handle on the magnitude.

Two interesting recent papers:
Noui and Roche "Cosmological Deformation of Lorentzian Spin Foam Models"
http://arxiv.org/gr-qc/0211109

Ichiro Oda "A Relation Between Topological Quantum Field Theory and the Kodama State"
http://arxiv.org/hep-th/0311149
Oda's paper came out last month and has a significant final sentence (at the end of the Conclusions section) on page 7:
"Of course, one of the big problems in future is to clarify whether the Lorentzian Kodama state is normalizable under an appropriate inner product or not."

Several months earlier Edward Witten had written that the state was not normalizable under the inner product which he (Witten) apparently considered appropriate and Oda seems to suggest here that this was inconclusive---the problem is still open. Some version of the Kodama state seems to be intermingled with the cosmological constant in these discussions and there seem to be some riddles involved here that interest good minds.

Perhaps answers to some of your questions could come out of this eventually. If the CC plays key roles at both large and small scale in quantum gravity (loop theory and spin foam models both) then the theory may eventually get a grip on it. Lambda is basically a GR thing, so successfully quantizing GR should give some handle on it, one would imagine.

Thanks a lot m8! I really appreciate your efforts in locating all these monumental references (sure makes for a good read!).

If you're interested in grappling with that idea yourself, here's a reference to that paper:
http://arxiv.org/hep-th/0306108

Thx again :)

 

[marcus]

[edit: alex I just saw your link to the Lisa Randall paper and immediately went and read it---I even think I understood some of it! It is short and limited in scope so not too hard to read. Thank you for the link.]

I had some more thoughts prompted by your question and made the following notes. Now I don't know whether they are needed. Perhaps, because they are very iffy and speculative, I should erase them. I may indeed do that, but for now, for what its worth, I will leave them up.

the CC seems to be a deformation parameter in the geometry of space,
specifically a deformation of the symmetry groups. For example
SL(2,C) becomes the (q-deformed) quantum group SL_q.
There are various notations for it.

Numerically here is how Lambda is related to q. If you express Lambda as energy density in PLANCK UNITS then it is a certain dimensionless number which turns out to be 0.8E-123
that is 0.8x10^-123
I believe it is an interesting number and obviously it is positive and very close to zero. And if you raise e to that number and get
exp(0.8E-123) it will be very close to one. That is q.
q = exp( 0.8x10^-123)

q is so near to one that when you do noncommutative geometry the numbers ALMOST commute. Everything is almost the way you would expect it to be, or Euclid or Newton or Laplace would expect, except not quite---but very close. As close as q is close to one.

So q deforms the Lorentz group and causes speeds to be quantized and makes the spin network quantum states of space be just slightly different and all that stuff. It is strange and I am trying to get used to this way of thinking about CC.

People accustomed to thinking of nature as fields and forces in flat Minkowski space will generally prefer to think of CC not as a geometrical deformation parameter but as an energy density, like the various notions of vacuum energy. I suspect that may not prove a productive way to think about it, in the longterm.

Minkowski space is a static background that doesn't have very interesting geometry, thinking of vacuum energy on fixed background is thinking "in the box", or so it seems to me

One way to think outside the box is to consider a dynamic geometry with the CC (alias q) as a deformation parameter----q is something that applies to the spin foams and networks that are the quantum states of space and spacetime in GR and it has a macroscopic (expansive, accelerating) effect on space and also a microscopic effect (quantizing the available levels of speed and relations between observers)

In a strange way the CC is also a kind of normalization parameter because it removes infinities in loop and foam models---sums and integrals that would otherwise diverge are controlled by introducing the q parameter and using q-deformed symmetry groups.

Another place where q-deformed groups ("quantum groups") come up is in Noncommutative Geometry. This is one of a family of approaches to quantum gravity which (unlike string theory) actually attempt to quantize the original background independent GR, which in string contexts is generally seen as too difficult to quantize.

My impression is that these non-string theoretical approaches to quantum gravity are converging, and the deformation parameter q (alias the cosmological constant) seems to be involved in their convergence. The links in the previous post may supply some corroborative detail.

As I see it your question is very "leading edge" and can only be answered in a very unclear speculative way, at the present time, but of course someone else may have an authoritative cut-and-dried answer! Anything is possible on this forum! My thinking about CC is still extremely tentative and speculative, in any case. Only my impressions, offered with no sense of certainty.

 

[meteor]

Of course that the cosmological constant is not the only possibility for dark energy; there are propossals for a evolving scalar field like quintessence, or k-essence. I have even recently read about one model that eliminates the necessity of dark energy to explain the acceleration of the universe: is called the Cardassian model and the acceleration of the universe is explained by modifying the Friedmann equation
But returning to the subject of the thread, I don't like the idea of cosmological constant. It assumes that spacetime is infinitely stretchable. How can be spacetime infinitely stretchable? It does not makes sense to me. I prefer the idea of a evolving scalar field. I really think that this evolving scalar field that is causing the acceleration of the universe is the same inflaton that drove inflation

 

[alexsok]

Marcus: Thanks for elucidating so gracefully this hounding problem (i think i understood the essence of your words, or at least most of it ... that is an interesting area of research and I'm connived of the prospects it could bring forth, based on your outlook.

meteor: thanks for mentioning the k-essence and the Cardassian model, going to read up on both :)

 

[selfAdjoint]

marcus

So q deforms the Lorentz group and causes speeds to be quantized and makes the spin network quantum states of space be just slightly different and all that stuff. It is strange and I am trying to get used to this way of thinking about CC.

Do you have references you like more than others for this q-deformed dynamics? Baez has a lot of stuff on it, but I find that however much I like his stuff I can't learn from it. I have an anti-cuteness gene I guess.

I'm currently reading Douglas & Nekrasov's http://arxiv.org/PS_cache/hep-th/pdf/0106/0106048.pdf , it was on Peskin's most-cited list and I can see why. It's an excellent introduction to the concepts and their application over a broad number of physics areas.

 

[marcus]

Originally posted by selfAdjoint
marcus

Do you have references you like more than others for this q-deformed dynamics?

I'm currently reading Douglas & Nekrasov's
http://arxiv.org/hep-th/0106048
... excellent introduction to the concepts and their application over a broad number of physics areas.

No I DONT have a reference I like for this! I am glad to get your recommendation for the Douglas/Nekrasov paper and will look at it immediately.

I do not mind "cuteness" when people are trying to explain, the way Baez does. At least I think I don't mind it, maybe in moderation. But I have not yet seen Baez explanations, so I would appreciate any link to them too if not too much trouble to get.

the whole noncommutative thing actually comes as a shock and a surprise to me. It disappoints me that Nature would do something like that to us. My only comfort is to cling to the belief that any deformation parameter that matters will be very very close to one, so that the deformation and the noncommutative stuff will be essentially imperceptible.

The only reason I want to pursue it is that I am a watcher and a follower. People I respect seem to be venturing into it. So I have to try to. But it seems like a jungle full of poisonous snakes.

I am totally amazed and impressed by Buffenoir, Roche, Noui being able to do harmonic analysis and get the irreducible representations of q-deformed groups. Representation theory for things that arent even really groups! It is very intimidating, or seems so at the moment.

 

[marcus]

selfAdjoint,

I had a look at Douglas/Nekrasov and while it does not seem to be quite the right introduction for my purposes it might nevertheless be just right for 3 or 4 other people at PF. So you might be able to start a good thread around that paper.

alejandro rivero ("arivero") at Zaragoza in spain used to post a lot at PF and I think he has had some personal contact with Alain Connes or has hung out with some of Connes friends.

Meteor and Ambitwistor and Lethe are here now and might like to take a collective stab at noncommutative stuff, via Douglas/Nekrasov.

For my own part, I still have to find an intuitive way into the subject that I can follow. I see people getting results and going places with it and I realize it must be interesting but I can't yet catch the wave. Like standing on the beach and watching other people surf.

I believe there may be a basic philosophical reason why coordinates do not exactly commute----a kind of HUP built into space itself

One cannot pin down both the position and momentum of a particle (says HUP)

One cannot pin down both the X and the Y of a position (? what can this mean?)

If you have any really basic intuition please share it!

 

[marcus]

Originally posted by meteor
It assumes that spacetime is infinitely stretchable. How can be spacetime infinitely stretchable? It does not makes sense to me.

But the pre-1998 zero CC open universe model was already destined to expand without limit. The observed average density did seem to be less than the critical density and so many people assumed the universe was open or flat and would expand forever. So that seems like "infinitely stretchable" already without a positive CC. I would like to understand your objection to a positive CC, but I am not getting it yet.

On the other hand, I do understand wanting to allow for the possibility that this constant is not really constant, but can evolve.
Perhaps very far in future it could get even closer to zero or it could possibly go negative!
But thinking of it as constant in space and time seems now to be at least a good approximation that people are finding useful.