Lattice refining loop quantum cosmology, anisotropic models and stability

In summary, Bojowald has developed a lattice refining loop quantum cosmology model that puts special emphasis on geometrical areas to determine the vertex number. This model is in general refined by adding new vertices when acting with the Hamiltonian constraint, which is in turn proportional to volume. Although the same principle applies to the all/any curved space, it has not been explored yet how to add new vertices as the volume increases and you get farther from the center of gravity. Eventually, someone will explain where the vertices come from and where they go.
  • #1
jal
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CONGRATULATIONS TO Martin Bojowald!
http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.1137v1.pdf
Lattice refining loop quantum cosmology, anisotropic models and stability
Martin Bojowald∗
09 April 2007
Such lattices are in general refined by adding new vertices when acting with the Hamiltonian constraint.
It has a vertex number proportional to volume, which is a limiting case not realized by known full Hamiltonian constraints, and puts special emphasis on geometrical areas to determine the vertex number.

Standard Theory SU(3)xSU(2)xU(1).…. String …. Have not done it. He is the first to address the Inverse Square Law.
The same principle applies to the all/any curved space. You got to add new vertices as the volume increases and you get farther from the center of gravity.

Eventually, someone will explain where the vertices come from and where they go.
jal
 
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  • #2
Good find, Jal.
I think you are right to spotlight this one.

I think this relates to the paper you started a thread about earlier---this thread:
https://www.physicsforums.com/showthread.php?t=163371

The earlier paper (29 March 2008) is by Bojowald solo, and may actually be based on more recent research. Sometimes a joint paper with several authors takes longer to wrap up and get posted so things come in a bit out of chronological order. but that doesn't matter.

I think this one is CONTRIBUTORY in some sense, to what he was talking about in the earlier paper you mentioned, titled: "...Physical Solutions of Quantum Cosmological Bounces"
http://arxiv.org/abs/gr-qc/0703144

==========================
BTW a guy who has co-authored papers with Bojowald, named Parampreet Singh, is giving an invited talk on Loop Quantum Cosmology at the big APS (American Physical Society) meeting this month in Florida.

If I remember correctly, his co-authors in the paper you just mentioned---Dan Cartin and Gaurav Khana---gave a paper at last year's April meeting.

Just as a side comment, I'd judge that Bojowald is a good person to collaborate with. His line of research is hot---and he doesn't monopolize the limelight.
 
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I'll try to give some perspective on Bojowald's line of research.

Perspective is needed in part just because one wants to not overestimate the importance of anyone paper.

To put it in larger context, "everybody" (even string theorists :smile: ) would like to get rid of the Bang singularity.
Singularities don't occur in nature, they are by definition the failure of some theory. The Bang singularity is a failure in General Relativity, where you are evolving back in time using cosmologists' GR-derived Friedmann model, and at a certain point the model fails and blows up---so time-evolution stops for that model at a certain point as you go back.

"Everybody" would like to see a model developed that would duplicate the good stuff of Gen Rel (where it doesn't break down) but would not fail--a model where time evolution keeps on going to before the beginning of expansion.

The LQC model developed by Bojowald and Ashtekar and numerous co-workers is the first major success along these lines. So it has attracted a lot of interest. This was the reason the Kavli ITP (a string stronghold) invited Bojowald to co-organize that January 2007 workshop. The main thing the workshop did was give exposure to the LQC people (Ashtekar Bojowald Thiemann) and let string folks get a taste of it and ask questions.

What Bojowald is struggling with now is extending the success of LQC to something more like the full LQG theory. To do this he may actually have to transform LQG. It may involve exploring various blind alleys. It may have to be done gradually---by relaxing the simplifying restrictions step by step.

We don't know how this is going to play out. Anything could happen.
I'll try to organize my thoughts about it and say some more.
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Oh, I think Jal has this link, but in case anyone else is reading here is the KITP workshop
http://online.kitp.ucsb.edu/online/singular_m07/

to get it you just have to google "kitp spacetime singularities", so there's no need to save the URL
 
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1. What is lattice refining loop quantum cosmology?

Lattice refining loop quantum cosmology (LRLQC) is a theoretical framework that combines elements of loop quantum gravity and lattice field theory to study the evolution of the universe at a very small scale. It aims to address some of the limitations of traditional cosmological models, such as the singularity problem and the lack of a quantum description of spacetime.

2. How do anisotropic models differ from isotropic models in cosmology?

Anisotropic models in cosmology consider the universe to have different expansion rates in different directions, as opposed to isotropic models which assume a uniform expansion in all directions. This allows for a more realistic description of the universe, as it allows for variations in the density and distribution of matter.

3. What is the significance of stability in LRLQC and anisotropic models?

Stability in LRLQC and anisotropic models refers to the ability of the model to produce consistent and predictable results under various conditions. In the context of cosmology, this is important as it allows us to make reliable predictions about the evolution of the universe and test the validity of the model.

4. What are some potential implications of lattice refining loop quantum cosmology and anisotropic models?

LRLQC and anisotropic models have the potential to provide a more complete and accurate understanding of the universe at a quantum level. They could also help to resolve some of the open questions in modern cosmology, such as the nature of dark matter and dark energy, and the origin of the universe itself.

5. How is lattice refining loop quantum cosmology related to other theories in physics?

Lattice refining loop quantum cosmology is closely related to other theories in physics, such as loop quantum gravity and lattice field theory. It also incorporates concepts from general relativity and quantum mechanics. By combining these different approaches, LRLQC aims to provide a more comprehensive and unified understanding of the universe.

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