Time zero glitch fades out/less need for inflation

[marcus]

Ashtekar "Mathematical Structure of Loop Quantum Cosmology"
http://www.arxiv.org/gr-qc/0304074

It's with co-authors Martin Bojowald and Jerzy Lewandowski
and the date is June 9, 2003 and its 29 pages with references

Ashtekar and company have an ongoing program to quantize the geometry of spacetime, that is to quantize the equations of general relativity and around ten papers have been published or submitted so far about the fact that the singularity goes away when you quantize GR.

General Relativity has this famous glitch at time zero where some
parameters "blow up" i.e. go to infinity so that you can't calculate with the model back to zero-----and certainly can't calculate back before. this is considered to be a failure of the equations.
"Big Bang" is a euphemism or a hand-waving gesture which by giving a name to it conceals the breakdown of the mathematics.
They could as well call it General Relativity's "great glitch".

In 2001 one of Ashtekar's postdocs discovered that when you quantize the model-----to get a kind of quantized Friedmann equations (assuming isotropy or homogeneity and including matter if desired)----then the glitch went away.

So he found himself staring at a pre-zero universe collapsing and then evolving right thru where the old glitch had been and then beginning to expand and become our universe.

So there has been a lot of activity, a lot of research action around this, since 2001.

Now Ashtekar has weighed in and had his say about it in this paper I gave the link to and although a lot of the paper is rather technical (making use of "almost periodic functions" and the "Bohm compactification of the real line" and making references to Russians like Gel'fand) it also has some nice philosophical overview parts for non-technical enjoyment.

So I am posting a thread on this paper for that reason and also because removing the glitch at time zero seems to reduce the need for "Inflation Scenarios".

The flatness would have been there because in either a matter-dominated or radiation-dominated universe flatness is PRODUCED by collapse. There is a nice formula about this which I will copy from Lineweaver in a followup post.

The equilibrium of temperature between one part of space and the other would have had time to emerge already before time zero---so inflation is not needed as a rather extreme kludge to fix up that either.

No disrespect to the Brilliant Minds like Guth and Linde who thought up inflation but removing the glitch seems to change the intellectual landscape so that having inflation in the first picosecond after time zero is no longer such an urgent requirement----and it is still just a scenario, nobody having come up with a magic "inflaton" to make it happen or a proof that it ever actually did happen. So it may have happened or it may not have, but now that does not seem to be such a burning issue.

 

[thermonuclear]

Marcus, I had a question regarding LQG cosmology.

I asked you about creation of matter, as during inflation, and you told me that LQG removes the singularity and describes the universe prior to time cero in a collapsing mode. Therefore, there is no need for creation. This seams indeed a more intuitive way to explain the whole thing.

But, when we are talking about a collapsing mode: does this mean a Big-Crunch, or this may be also some other kind of collapse, like a black hole? If Big-Crunch, the question is how this fits with the fact that the current observations reveal an open universe. I mean: the process (Big-Bang, Big-Crunch) should not be perfectly reversible.

Regards.

 

[marcus]

Originally posted by thermonuclear
Marcus, I had a question regarding LQG cosmology.

I asked you about creation of matter, as during inflation, and you told me that LQG removes the singularity and describes the universe prior to time cero in a collapsing mode. Therefore, there is no need for creation. This seams indeed a more intuitive way to explain the whole thing.

But, when we are talking about a collapsing mode: does this mean a Big-Crunch, or this may be also some other kind of collapse, like a black hole? If Big-Crunch, the question is how this fits with the fact that the current observations reveal an open universe. I mean: the process (Big-Bang, Big-Crunch) should not be perfectly reversible.

Regards.

I have similar questions and there are several parts of this that I don't understand. So I would appreciate your help in understanding it if you get interested in this. First of all, here are some more references in case you want to look at them.

1. This article has pictures-----a wave-function passing through time zero:
Homogeneous L.Q.Cosmology (March 2003, see page 16)
http://www.arxiv.org/gr-qc/0303073

2. This article provides a recent general overview from a seminar at Univ. Iztapalapa. One of the co-authors is Hugo Morales-Tecotl and the other is Bojowald. Pages 21, 22 describe the boundedness of the inverse scale factor and give a graphic comparison with its classical behavior.

Cosmological Applications of L.Q.Gravity (June 2003)http://www.arxiv.org/gr-qc/0306008

3. This third article examines the isotropic case and describes the behavior at time zero in figurative language as a "bounce". I do not believe this is meant as a mechanistic explanation but rather as a graphic intuitive description of the behavior-----a collapsing phase which reverses and becomes an expanding phase at time zero.

Isotropic L.Q.Cosmology (February 2002)
http://www.arxiv.org/gr-qc/0202077

4. This fourth article incorporates a scalar field
Isotropic L.Q. Cosmology with Matter
http://www.arxiv.org/gr-qc/0207038
The purpose is to illustrate how the quantization regulates
pathological behavior observed in other models where wave
functions develope infinitely many oscillations near the singularity.

I believe that the analysis here does not contemplate the collapse of space to a "point". The singularity that is removed is infinite in extent, as I read it, in every case. The important thing is passage through zero while the curvature, the density, the oscillations (and so on) remain bounded---the quantum operator corresponding to the inverse scale factor is diagonalized with bounded eigenvalues.

As I see it the best and most authoritative summary is given in the June 2003 paper by Ashtekar, Bojowald, and Lewandowski
which I gave the link to earlier. This is because Bojowald is just a postdoc, while both Ashtekar and Lewandowski are senior people going back to the 1980s. The thoroughness with which the singularity is removed is surprising enough that I require some confirmation from "heavies" of the field. So I will post that link again:

Mathematical Structure of L.Q.Cosmology
http://www.arxiv.org/gr-qc/0304074

Now as to your question regarding a "Big Crunch"...of course you realize I am not an expert and am just trying to learn about quantum cosmology, but I will tell you what I think:

I only know of the "big crunch" idea in the case of a closed, or finite universe. This is not what is being studied here.
A closed universe, having at all times a finite volume, can appear from a point and then recollapse down to a point.
But this is not the model being studied!
Ashtekar et al (the June 2003 article I linked to) are very explicit about this on page 3, where they say that the spatial manifold M is topologically equivalent to R³.
So what is going on seems to be very different from the old idea of the closed universe big crunch and big bang. But to learn what it is I must refer you to the papers (of which there is a growing number, I have provided links to only a sampling of them!)

 

[thermonuclear]

OK marcus, thanks for the answer. I'll surely take a look to the papers, but I'm not sure whether I'll be able understand them (I'm just only beginning to understand the principal ideas of LQG).

BR.

 

[marcus]

Originally posted by thermonuclear
...(I'm just only beginning to understand the principal ideas of LQG).

The best introductory treatment I know is by a guy at Munich
(Marcus Gaul) together with Carlo Rovelli.

http://www.arxiv.org/gr-qc/9910079
"Loop Quantum Gravity and..."

It is 52 pages and unusually careful and clear. It is definitely an introduction to the subject and not a survey or something else. They guide you slowly step by step.

If you feel like learning the subject, I will help. Print the Gaul/Rovelli paper out and we can go through it, just ask about things you don't understand and I or someone else can try to explain.

then once you are thru that 50-page basic treatment you can
read quantum cosmology or spin-foam research or whatever you want and you will understand much more because you have spent some time on the basics.

Let me know if you want to do that. If you do not reply I will assume you do not want to---which is fine also.

 

[drag]

Greetings !

I just wanted to note that in a recent article that I read
it was said that recent astronomical observations
intended to detect distortions of the light coming from
distant sources as a result of theorized space-time quantization
failed to find such distortions and put considrable
constraints on the possibility of a quantized space-time.

Live long and prosper.

 

[marcus]

Originally posted by drag
Greetings !

I just wanted to note that in a recent article that I read
it was said that recent astronomical observations
intended to detect distortions of the light coming from
distant sources as a result of theorized space-time quantization
failed to find such distortions and put considrable
constraints on the possibility of a quantized space-time.

Live long and prosper.

Hello drag, please post the link to that article if you can find it!
I have seen several papers in which observations were used to
narrow the bounds on some parameters in LQG and I find the business pretty interesting, so would be glad to look at the one you found too (if it is not one I've already seen)

Observations of cosmic rays, gamma ray bursts, polarization in light from distant galaxies, and apparently even synchrotron radiation from Crab nebula have all been used to narrow the bounds on a parameter denoted by alpha (in what are described in a recent summary of these investigations as two different theoretical possibiliites or scenarios A and B)

These are summarized on page 19 of
http://www.arxiv.org/hep-th/0303185

which has references to a dozen or so papers
in which observations afford a chance to check and refine
the model of quantum general relativity.

It is pretty exciting, I find, and in a sense quite surprising since
for a long time it was assumed that Planck-scale effects were
inaccessible, making theories hard to test. What these tests show is that this is not the case and we can expect increasingly refined tests over the next 5 or 10 years. I noticed quite a few papers on this were delivered at this summer's quantum gravity conference at Penn State---a sign that LQG is beginning to interest observational astronomers and the people who allocate telescope time etc.

Have a look at the link I mentioned----on page 18 it has a description of what the parameter alpha is and also says what the two scenarios are.

 

[drag]

Eeh... Sorry, I can't quite remember where I read it
or I would've posted the link above already, but it
was just a general article for the general public with
no real data. I think you should look for this study on
arXiv (should be a recent one) to get detailed technical info.

Live long and prosper.