"Quantum Gravity and Inflation"---a new paper

marcus

The following paper appeared today in arxiv preprints

Stephon Alexander et al
"Quantum Gravity and Inflation"
http://arxiv.org/hep-th/0309045

The paper could be important. By way of detail, it has
been submitted to Physical Review Series D
Alexander is a member of the SLAC high energy physics group
and Stanford's ITP (Institute for Theoretical Physics)
Previously he was at London's Imperial College and at Brown.
In the past he has published string-and-brane-type research and
also in noncommutative geometry (Shawn Majid is at Imperial College) but in the present article is
working in an area closely related to Martin Bojowald's loop quantum cosmology.
Bojowald also found that loop quantum cosmology generates an inflationary period---as well as eliminating the big bang singularity.
Alexander, Malecki, and Smolin refer to this paper of Bojowald "and the references therein"

Bojowald et al "Cosmological Applications of Loop Quantum Gravity"
http://arxiv.org/gr-qc/0306008

It could be an exciting season in loop quantum gravity as applied to cosmology----or maybe one should say QGR (quantum general relativity) as applied to big bang, inflation etc. We seem to need some general term for quantizations of general relativity (LQG is representative but there are discrete or lattice approaches under active investigation and also there is the spin foam approach.) So maybe one should broaden the category to include a family of related lines of research all aimed at quantizing general relativity. Anyway it is possible for someone like Alexander to get out of strings and branes and get into QGR cosmology. The paper looks important to me, but judge for yourself

marcus

PF policy encourages only brief quotes from published material so here are a few sentences at the start of the abstract of the Alexander et al paper "Quantum Gravity and Inflation"

"Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes.

The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly...

...Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation...."

I think it is pretty interesting and am putting Stephon Alexander on my list of young postdocs to check up on now and then to see what they've been doing.

Martin Bojowald who already earlier this year derived inflation from the loop quantum gravity early universe model is already on my list. This new paper seems to get the same qualitative results but in a slightly different way.

jeff

Take a look at this very brief (3 pages) paper. The author proposes yet another possible way to avoid the SU(2) → SO(3) problem by replacing SU(2) with the supergroup Osp(1|2). In this case, the immirzi parameter is twice the usual non-supersymmetric value, one consequence of which is that, effectively, only integer spins contribute to area.

http://xxx.lanl.gov/abs/gr-qc/0309018

Btw, I found equation (20) - particularly it's left-hand side - oddly moving, though I couldn't quite put my finger on why.

marcus

my compliments on this post
the BTW comment is charmingly put and very funny
I have immediately downloaded and printed out the paper
which is by a couple of Beijing guys
and have, of course, given great attention to equation (20)

selfAdjoint

Wow, an interesting season for sure. Marcus, I think maybe Bojowald's paper is the one described by Baez in a past TWF which used expansion of the universe as a time coordinate in QGR, solving the time problem, and was able to discuss states before t=0.

marcus

Hi selfAdjoint,
if you come across a link again to Baez discussing Bojowald please post it---you may have told me about it earlier but I lose track of links and it would be good to have it.

Just for easy reference, in case anyone wants them, I will list some of Bojowald's recent loop quantum cosmology articles

Absence of Singularity in Loop Quantum Cosmology
gr-qc/0102069
Isotropic Loop Quantum Cosmology with Matter
gr-qc/0207038
Initial Conditions for a Universe
gr-qc/0305069
Inflation from Quantum Cosmology
gr-qc/0206054
Loop Quantum Cosmology, Boundary Proposals, and Inflation
gr-qc/0303072
Isotropic Loop Quantum Cosmology
gr-qc/0202077
Cosmological Applications of Loop Quantum Gravity (with Morales-Tecotl)
gr-qc/0306008
Mathematical Structure of Loop Quantum Cosmology (with Ashtekar and Lewandowski)
gr-qc/0304074

These are in no particular order.
What I am especially interested in seeing now is responses to this work in the QGR community in the form of papers that in some sense repeat this line of investigation and get similar results, and which reference Bojowald.

the paper by Stephon Alexander et al was one example
Quantum Gravity and Inflation
hep-th/0309045

there has also been one by Golam Hossain (Inst. Mathematical Sciences, India) that appeared recently
"Hubble Operator in Isotropic Loop Quantum Cosmology"
gr-qc/0308014

and an interesting series by Gambini and Pullin---for a sample:
Discrete Quantum Gravity: Applications to Cosmology
gr-qc/0212033
(Gambini is in Montevideo, Uruguay)

Bojowald's work has also been discussed and referenced in survey-type writing by several other people such as Ashtekar and Rovelli, but I am looking more for articles which parallel or continue this line of research.

selfAdjoint

Baez's discussion of Bojowald's recent work is in This weeks Finds #167. (Down near the bottom). Baez lists Bojowald's papers in #165.

marcus

thanks much for the reference to Baez "This Week's Finds" #167 discussion of Bojowald work----that was 2001 so I imagine the papers he's referring to are earlier. The one's I gave links for are mostly 2002 and 2003 so there wont be much overlap.

I shall quote snatches of Baez (this is from the Usenet newsgroup he hosts called "sci.physics.research")

"...Bojowald's progress comes from looking at "minisuperspace models", where we assume the universe is highly symmetrical - as people often do in cosmology. This allows him to tackle the problem of time by treating the volume of the universe as a notion of time. It's like having one aspect of the system you're studying be the clock that you use to see how other things change. This idea per se is not new; what's new is carrying it out in the framework of loop quantum gravity. In loop quantum gravity volume is discrete... so Bojowald's "clock" ticks in discrete steps. By adapting Thiemann's formula for the Hamiltonian constaint to this highly symmetrical context, he can write it as an evolution equation saying how other observables change as a function of the volume of the universe. Since volume is discrete, this equation is a difference equation rather than a differential equation.

He can solve this equation on the computer... and he finds that even when the universe is very small, on the order of the Planck length, it closely mimics the classically expected behavior. However, there is no singularity at t = 0, or more precisely, at zero volume..."

As always, Baez knows how to put things clearly.
since 2001, when he wrote that, things have only gotten better.