What resources are available for studying higher dimensional quantum cosmology?

[ylping]

I going to to study the quantum cosmology. who can give me some advice and supply some papers and books?

Thanks.

 

[hellfire]

An introduction to quantum cosmology
http://arxiv.org/abs/gr-qc/0101003

This is an introduction to the quantum cosmology derived from the canonical quantization of general relativity (therefore somehow a bit out of date, I think). Currently I am very interested in this and I am trying to understand the basics. The paper gives a very good overview, but lots of aspects are treated only superficially.

 

[marcus]

I going to to study the quantum cosmology. who can give me some advice and supply some papers and books?

Thanks.

This post is not advice. I am not recommending anything yet. I just want you to know that
a major development in quantum cosmology is LQC.
Loop Quantum Cosmology
This is application of LQG to cosmology with simplifying assumptions that cosmologists usually make (such as large scale homogeneity).
LQC is MUCH EASIER mathematically than the full theory of LQG, because the universe is assumed to be homogeneous, and sometimes also isotropic. the model is therefore more uniform and symmetric---making it more manageable. so there was rapid progress.

Because of rapid progress in LQC, in the period 2001 through 2004, people were drawn into this line of research (an order of magnitude more LQC researchers in 2004 than in 2001). I wouldn't call it crowded yet though. I estimate that research output increased at least 50 percent between 2003 and 2004.

To illustrate: these searches will bring up some, but not all, of LQC papers from 2003 and 2004 (and also a few imposters: extra stuff that comes up by mistake). Although not precise, the raw numbers are indicative of the growth. 11 papers come up for 2003 and 21 papers come up for 2004


2003
http://arxiv.org/find/grp_physics/1...+AND+loop+quantum+abs:+gravity/0/1/0/2003/0/1

2004
http://arxiv.org/find/grp_physics/1...+AND+loop+quantum+abs:+gravity/0/1/0/2004/0/1

However I see that leaders in LQC, such as Martin Bojowald, are beginning to move into studying LQG QUANTIZATION OF BLACK HOLES. This represents a move of quantum gravity people away from focusing on things like big bang and inflation and towards a new focus, on gravitational collapse and possibly black hole evaporation.

I am still not recommending or advising. Just mentioning some details of the picture.

 

[marcus]

Ylping,
what level of study are you talking about?

Where are you in school? High school, university, graduate school?

Where do you want studying quantum cosmology to lead you?

I will give you some links, but since I do not know your situation and needs, they might possibly be wrong for you.

 

[marcus]

----BASICS OF LQC---
http://arxiv.org/abs/gr-qc/0505057
Elements of Loop Quantum Cosmology
Martin Bojowald
30 pages, 4 figures, Chapter contributed to "100 Years of Relativity - Space-time Structure: Einstein and Beyond", Ed. A. Ashtekar (World Scientific)

"The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to describe them properly, and one has to refer to quantum gravity. A complete quantization of gravity has not yet been developed, but there are many results about key properties to be expected. When applied to cosmology, a consistent picture of the early universe arises which is free of the classical pathologies and has implications for the generation of structure which are potentially observable in the near future."

-----SURVEY ARTICLE WITH SECTION ON QC, discusses several types, not just LQC------
http://arxiv.org/abs/gr-qc/0508120
Quantum Gravity: General Introduction and Recent Developments
Claus Kiefer
21 pages, 6 figures, invited contribution for "Annalen der Physik"

"I briefly review the current status of quantum gravity. After giving some general motivations for the need of such a theory, I discuss the main approaches in quantizing general relativity: Covariant approaches (perturbation theory, effective theory, and path integrals) and canonical approaches (quantum geometrodynamics, loop quantum gravity). I then address quantum gravitational aspects of string theory. This is followed by a discussion of black holes and quantum cosmology. I end with some remarks on the observational status of quantum gravity."

---------FOR BALANCE, ANOTHER SURVEY, critical of LQC---------
http://arxiv.org/abs/gr-qc/0412026
Quantum Cosmological Models
D.H. Coule
71 pages
Class.Quant.Grav. 22 (2005) R125-2308

"We contrast the initial condition requirements of various contemporary cosmological models, including inflationary and bouncing cosmologies. Various proposals such as Hartle-Hawking's no boundary, or Tunnelling boundary conditions are assessed on grounds of naturalness and fine tuning. Alternatively a quiescent or ``time machine'' state is considered. Extensions to brane models are also addressed. Further ideas about universe creation from a meta-universe are outlined.
We compare the recent loop quantum cosmology of Bojowald and coworkers with these earlier proposals. A number of possible difficulties and limitations are outlined."

-----DIFFERENT APPROACH, CDT, not discussed in the surveys-----
http://arxiv.org/abs/hep-th/0411152
Semiclassical Universe from First Principles
J. Ambjorn, J. Jurkiewicz, R. Loll
15 pages, 4 figures
Phys.Lett. B607 (2005) 205-213

"Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in the Euclidean sector of this theory is a bounce which satisfies a semiclassical equation. After integrating out all degrees of freedom except for a global scale factor, we obtain the ground state wave function of the universe as a function of this scale factor."

---MY FAVORITE, which some people would not recognize as quantum cosmology---

http://arxiv.org/abs/hep-th/0505154
Reconstructing the Universe
J. Ambjorn, J. Jurkiewicz, R. Loll
52 pages, 20 postscript figures

"We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time."

 

[ylping]

I study in graduate school. My major is higher dimension cosmology. I want to study the quantum cosmology with extra dimension. So I should know what had been done in standard model.

 

[marcus]

I study in graduate school. My major is higher dimension cosmology. I want to study the quantum cosmology with extra dimension. So I should know what had been done in standard model.

I cannot advise you because my reading is all in low dimension (mostly 4, some 2 and 3). You are probably thinking about string and brane. Maybe someone else here at PF will have advice.

One thing I can tell you is this. No one as so far studied the Loll CDT path integral in dimension 5 or higher.

All the work in causal dynamical triangulations is dimension 4 or less. So if you can understand how CDT works in dimension 4 and extend one higher dimension then you are automatically in new territory. But I have no way to tell if that is interesting or not.

Today Loll posted another paper on arXiv
http://arxiv.org/hep-th/0509010
"The Universe from Scratch"

The words " from scratch" means from simple primitive raw materials.
this is American slang. To make some bread, or cook some food, from scratch means to use basic unprocessed raw materials. To make it not-from-scratch means to use a pre-packaged convenient "mix"---frozen vegetables from the store already cleaned and cut-up, sugar and flour and seasoning bought from the store already measured and mixed.

the lazy person does not like to cook from scratch.

I think you are perhaps in China so I am telling you about our Slang words, a dialect you may not know.

This new paper of Loll is the best introduction so far to the CDT quantum gravity.

Good luck with your research, whatever you choose to do.