# The Ashtekar density (you've heard of the Chandrasekhar mass, now here's )

1. May 21, 2007

### marcus

Ashtekar's team at Penn State has been running cosmological BOUNCE simulations on the computer, studying many different cases.

A certain critical mass-energy density has emerged as important.

It does not depend on the value of the cosmological constant (some of their simulations are of realistic universes in the sense of having a positive cosmo constant)

It does depend on the value of the LQG immirzi parameter. The preferred value here is gamma = 0.2375

in case after case, whatever the particular detailed assumptions, when there is a contracting QG universe it will contract until the density is 82 percent of Planck density, and then (quantum gravity becoming repellent at high density) it will bounce, and re-expand.

Shouldn't we call this critical density the Ashtekar density?

2. May 21, 2007

### marcus

the definition of the Planck unit density is Planck unit mass per Planck length cubed, and that boils down to something very simple namely

$$\frac {c^7}{\hbar G^2}$$

and the Ashtekar density is a certain number multiplied by this. The number is

$$\frac {\sqrt{3}}{16 \pi^2 \gamma^3}$$

that is where you plug in gamma = 0.2375 (or if you are Alejandro Corichi you plug in 0.274 )

So the whole expression for the Ashtekar critical mass-energy density is

$$\frac {\sqrt{3}}{16 \pi^2 \gamma^3} \frac {c^7}{\hbar G^2}$$

That's where she bounces, folks. When that critical level of density is reached.

Last edited: May 21, 2007
3. May 21, 2007

### marcus

just in case you want to look at a paper
http://arxiv.org/abs/gr-qc/0607039
Quantum Nature of the Big Bang: Improved dynamics
Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh

this treats the most realistic case----spatial flat, positive cosmologica constant, matter of course.

but this other paper is nice too, it deals with cases where the universe has enough mass to stop expanding and re-collapse----so the bouncing goes on and on. in those cases also the same critical density triggers the bounce:

http://arxiv.org/abs/gr-qc/0612104
Loop quantum cosmology of k=1 FRW models
Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh, Kevin Vandersloot

both published in Physical Review D.

==============

If you happen to like "experimental physicist units" like GeV and the small length called a "fermi" also called a femtometer, then you might like to know what is the Planck energy density in those terms. The fermi volume is a cubic fermi.

At the LHC sometimes they plan to accelerate beams of heavy nuclei, like iron nuclei, instead of protons----and collide these nuclei at high speed.
This will achieve a buzzing swarm of gluons all going every whichway, as it were during a 'big bounce' of a universe, except the energy density won't be so high. It is estimated this will achieve an energy density on the order of ONE GeV per cubic fermi.

I read maybe 2-3 GeV/fermi3, something around that order of magnitude.

When you work it out, Planck energy density is 2.9 x 1078 GeV/fermi3
So Planck (and Ashtekar) is some 78 orders of magnitude higher density.

Last edited: May 21, 2007
4. May 21, 2007

### Wallace

Do you think this could ever be testable?

5. May 21, 2007

### marcus

With GR, one does not test every derivable result (including past and future) of the theory, one finds ways to test the theory in the present, with what one can observe at present.

With QG it will be similar. There is a new field called "QG phenomenology". they are looking at all the ways to derive predictions from various QG approaches so they can test them.

One big question now is whether the leading forms of LQG predict a signature that could be detected in the CMB. Another issue is whether this or that model predicts dispersion suppressed at Planck scale that could nevertheless be detected in GRB that have traveled over cosmological distances.

Ted Jacobson is one expert in QG testing, he has shot down some early forms of QG already using astronomical observations. You can find his papers (often with Stefan Liberati) on arxiv if interested.

An up-and-coming expert in QG phenomenology is Bee Hossenfelder. She will be giving the invited plenary talk on "QG phenom." at this summer's big LQG conference. It is a hot field. The German science foundations offered her a prestigeous Emmy Noether fellowship if she would return to Germany and set up and lead a QG phenomenology group at Uni Hamburg. But she turned down the Noether and chose to go to Perimeter Institute instead.

The point I think, Wallace, is you TEST THE THEORY AS A WHOLE however you can. If the theory predicts a bounce, and continues probing back into the past further than 14 billiion years, well you cant observe the bounce! That is not a way to test the theory because you can't go back and witness it.
But that does not stop you from testing the theory other ways, and perhaps falsifying it on empirical grounds if it is wrong.

Perhaps this is too simple an answer, and you already realize everything I am saying. If so repeat your question with a little finer resolution and I'll try to answer.

6. May 22, 2007

### marcus

Here is the Loops '07 website
http://www.matmor.unam.mx/eventos/loops07/index.html
When you get there, click on Program and in the list of plenary talks you can find
Sabine Hossenfelder: Phenomenological Quantum Gravity

Abstract: "The search for a satisfying theory that unifies general relativity with quantum field theory is surely one of the major tasks for physicists in the 21st century. During the last decade, the phenomenology of quantum gravity and string theory has been examined from various points of view, opening new perspectives and testable predictions. I will give a short introduction into these effective models which allow to extend the standard model and include the expected effects of the underlying fundamental theory. I will talk about models with extra dimensions, models with a minimal length scale and those with a deformation of Lorentz invariance. The focus is on observable consequences, such as black hole and graviton production and modifications of standard-model cross-sections."

Clicking on the title of one of the plenary talks will get the abstract.

7. May 22, 2007

### Wallace

Sounds good, yes what I was getting at is are there testable predictions other than things that just give us what we already think the very very early universe should be like. It appears from what you've said that there are, which is encouraging.

It's funny, real physicists (ones that play with real stuff in labs) think Particle Physics is not as robust as their work, since the data is always so model dependent. Particle physicists think Astronomy is a bit woolly since you can never verify your models and predictions about the nature of distant objects in a lab, astronomers think Cosmology is a bit woolly since you only have one thing you can look at (the universe) and every interpretation of it is highly model dependent. Cosmologists like Simon Driver think dark energy cosmologists are a bit woolly since you can never verify it in a lab or detect it directly. And then dark energy cosmologists (such as me) think QG is a bit woolly since it is very hard to check observationally....

It reminds me of a conversation I had once with a colleague. I was working on interacting dark energy - dark matter models and he said he didn't like them since they were 'ad hoc' yet their entire publication career was based on dark energy, which is nothing but ad hoc!

We live in interesting times....

8. May 22, 2007

### MeJennifer

I think the Barbero-Immirzi parameter is nothing but a fudge factor (to get the spin connections to work out). Raising this to some fundamental value is not physics but math play. I am just waiting for LQG to "derive" the value of lambda or the Hubble constant.

Looks like "the trouble with LQG" is right in the making.

Last edited: May 22, 2007
9. May 22, 2007

### marcus

Immirzi parameter is part of classical GR physics, before you get around to quantizing GR. It has effects which are observable in principle.

http://arxiv.org/abs/gr-qc/0505081
Physical effects of the Immirzi parameter
Alejandro Perez, Carlo Rovelli
3 pages, published in Physical Review D73 (2006) 044013

"...We show that in the presence of fermions, instead, the Immirzi term in the action does not vanish on shell, and the Immirzi parameter does appear in the equations of motion. It determines the coupling constant of a four-fermion interaction. Therefore the Immirzi parameter leads to effects that are observable in principle, even independently from nonperturbative quantum gravity."

Last edited: May 22, 2007
10. May 22, 2007

### MeJennifer

Here is a link to a posting from Baez on sci.physics.research where it is clear (at least to me) that it is simply fudge: The Immirzi parameter

Now after almost 6 years it apparently has been promoted to some fundamental parameter.

Alejandro Perez, Carlo Rovelli: "...We show that in the presence of fermions, instead, the Immirzi term in the action does not vanish on shell, and the Immirzi parameter does appear in the equations of motion. It determines the coupling constant of a four-fermion interaction. Therefore the Immirzi parameter leads to effects that are observable in principle, even independently from nonperturbative quantum gravity."

Yes, but all this hinges on whether this parameter makes any sense in the first place. I suppose for the cheerleaders it is now just a matter of waiting for Alejandro Perez and Carlo Rovelli to collect the Nobel price once this "done deal" is experimentally verified.

Just to be clear, the theory of general relativity has nothing to do with this. The fact is that attempts to quantize GR ran into big trouble under LQG, so the "solution" was to add some parameter.

Last edited: May 22, 2007
11. May 22, 2007

### marcus

Your info is out of date. Your Baez quote is from 2001 give us a break.
Don't know what 'big trouble' you mean specifically but lot's of progress in past couple of years overcoming various problems
(or maybe you are talking about Hamiltonian 'big trouble' encountered back in 1997, which led to spinfoam approach, but that's ancient history)

lot of popular misconceptions and mythology about 'LQG troubles'
you need to check recent sources.

Immirzi connection is a valid area of research in PURE GR
quite apart from LQG or any other quantum gravity.
Here is Mauro Francaviglia, prof at Uni Torino
http://www.francaviglia.it/
here is a recent paper (pure GR, no LQG)
http://arxiv.org/abs/gr-qc/0702134
On a Covariant Formulation of the Barbero-Immirzi Connection
13 pages
"The Barbero-Immirzi (BI) connection, as usually introduced out of a spin connection, is a global object though it does not transform properly as a genuine connection with respect to generic spin transformations, unless quite specific and suitable gauges are imposed. We shall here investigate whether and under which global conditions a (properly transforming and hence global) SU(2)-connection can be canonically defined in a gauge covariant way. Such SU(2)-connection locally agrees with the usual BI connection and it can be defined on pretty general bundles; in particular triviality is not assumed. As a by-product we shall also introduce a global covariant SU(2)-connection over the whole spacetime (while for technical reasons the BI connection in the standard formulation is just introduced on a space slice) which restricts to the usual BI connection on a space slice."

You don't have to be a cheerleader to realize LQG is making rapid progress these days, you just have to have your eyes open and not be in denial.

Last edited: May 22, 2007
12. May 22, 2007

### jal

As you have all seen, in my blog, I have my own unique way of asking a question. "The Immirzi parameter" and "bounce" are linked to minimum length.
If you want to have minimum length in your calculations then you got to stay consistent (black holes, big bang, quark confinement, H-dibaryon sphere, plaquettes, etc).
You cannot keep stratling the fence.
You have MINIMUM LENGTH or you don't. You cannot keep the old way of doing things.
As you can see in my blog, when you stay faithfull to minimum length, you get surprising paths.
Who is wrong? ME!!! :surprised
HOW?
JAL

13. May 22, 2007

### MeJennifer

This posting gives an excellent description on how this parameter initially got on the LQG stage. And it wasn't insight.

Last edited: May 22, 2007
14. May 22, 2007

### marcus

Perez and Rovelli's paper was peer-reviewed and published 2006 in Physical Review D, which is about as good as you can get for this kind of research.

Yes they found that the immirzi parameter has physical meaning quite apart from this or that quantization of GR.
Yes that contradicts what you think is implied by what John Baez said on the internet in 2001.

If you want to believe your interpretation of what Baez said on sci.physics.research in 2001 and not believe what Rovelli said in 2006, then I guess you can take it up with the editors and reviewers of Physical Review D.

There are a lot of popular misconceptions about LQG floating around. We probably need to have more discussion here about the actual state of QG research and its growing relevance to cosmology.

Last edited: May 22, 2007
15. May 22, 2007

### hellfire

From the abstract:

How shall I understand this? It seams widely accepted that the effective equations of LQC in the semiclassical regime change the equation of state of any kind of matter leading to a superinflationary phase with equation of state parameter w < -1. So it seams rather natural to me that bounces may occur at lower densities, why should this be a weakness?

Last edited: May 22, 2007
16. May 22, 2007

### marcus

I think one should focus on the collapse phase prior to the bounce----then inflation is not an issue. In the old model used to have some ambiguity about what conditions trigger the bounce. The 2006 improvement gets rid of that ambiguity.

In all the cases studied, regardless of differences in detail, the bounce always occurs when the critical density is reached. After that, what happens may be very different depending on assumptions. I may be overlooking something or a class of cases which are fundamentally different where this doesnt happen, and of course the model they are using has not beein observationally tested, but that's how I understand what he's saying.

Last edited: May 22, 2007
17. May 22, 2007

### jal

18. May 23, 2007

### hellfire

Why not? Those models that have a bounce in the semiclassical regime start expanding with an (super) inflationary phase. Actually, the bounce is due to the change of the equation of state of matter to w < -1. This, however, does not show up in every model, and those that pass through the semiclassical phase contracting without bouncing, do later bounce at the discrete regime. This is explained for example in gr-qc/0601085.

It would be great to know what this means exactly. Any idea?

19. May 23, 2007

### marcus

Hi hellfire,
I was in too much of a hurry yesterday when I replied to your question.
what I mean is, to simplify the discussion let's just look at the collapse phase.
WHILE it is collapsing, inflation is not a big issue.

With the old model, the bounce would get triggered at various different densities depending on the value of a parameter j (as I recall it) which was hard to make physical sense of. You ask why this was a weakness.

this is just as I remember it, I cant look back in the articles now, but as I remember it WAS a weakness because this parameter (I think called j) was an ambiguity and there was no obvious physical reality so that you could make sense of it. So it didn't seem to be a good thing that the answer, of when the bounce came, would depend on this.

Forgive me if I am misstating the situation. I don't want to take the time now to reference older papers but I remember, last year, being very glad to see that the bounce was always coming consistently at when the density reached 80 percent of Planck.

the quantum corrections to gravity, that change attraction to repulsion, SHOULD intuitively kick in when a certain high curvature or high density is reached, my feeling is. It is physically imaginable. So it was reassuring, back in mid 2006, when they began to get these results in their computer modeling.

You may be thinking about something at a deeper level which I haven't grasped. If I am missing some important reason that the bounce should be able to be triggered at different densities, please explain further.

right now in the computer simulations in the k=1 (finite universe) case, the bounce can be triggered when the contracting universe reaches different SIZES depending on how much matter you put in to start with-----but it tends not to vary what density triggers it.

I agree with you that it is quite interesting that, as soon as expansion begins, there is a kind of natural inflation that may kick in. It doesnt seem to be something you need to put in by hand. I see by some of your comments that you have been looking at this.

For me that is a whole other issue, but a very interesting one. One of the reasons one WANTED inflation in the first place was because of the horizon problem but it seems to me now, with a bounce, that there has been prior time for equilibrium to be achieved so perhaps the horizon problem is not so pressing.

Last edited: May 23, 2007
20. May 23, 2007

### hellfire

You are right about the ambiguity parameter, I didn't remember that. The paper is too dificult for me anyway so I have a hard time to extract the phenomenological aspects from it.