Bounce derived in spinfoam cosmology

[marcus]

http://arxiv.org/abs/1010.1258
Big Bounce in Dipole Cosmology
Marco Valerio Battisti, Antonino Marciano
5 pages
(Submitted on 6 Oct 2010)
"We derive the cosmological Big Bounce scenario from the dipole approximation of Loop Quantum Gravity. We show that a non-singular evolution takes place for any matter field and that, by considering a massless scalar field as a relational clock for the dynamics, the semi-classical proprieties of an initial state are preserved on the other side of the bounce. This model thus enhances the relation between Loop Quantum Cosmology and the full theory."

This is part of a new development in the application of LQG to cosmology. The earlier application followed a Hamiltonian approach and the model was symmetry-reduced (homogeneous and isotropic). In 2008 and 2009 a significant effort began to link cosmology to the full theory and to relax assumptions of uniformity. Instead of limiting this to Hamiltonian LQG, the researchers applied the covariant (spinfoam) version of the theory.

As far as I know, this Battisti-Marciano paper is the first time that the spinfoam version has reproduced the Big Bounce result achieved earlier with Hamiltonian LQC.

I'll give some background.

There is this paper, published in Physical Review D of March 2010. You can see clearly here the move in Loop Cosmology away from isotropy and homogeneity. A number of LQC papers have been about quantum versions of Bianchi I and Bianchi IX universes (which are anisotropic).

http://arxiv.org/abs/0911.2653
Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
Marco Valerio Battisti, Antonino Marciano, Carlo Rovelli
(Submitted on 13 Nov 2009)
"We develop the 'triangulated' version of loop quantum cosmology, recently introduced in the literature. We focus on the 'dipole' cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model. We show that the model is rich enough to describe the (anisotropic) Bianchi IX Universe, and give the explicit relation between the Bianchi IX variables and the variables of the model. We discuss the possibility of using this path in order to define the quantization of the Bianchi IX Universe. The model contains more degrees of freedom than Bianchi IX, and therefore captures some inhomogeneous degrees of freedom as well. Inhomogeneous degrees of freedom can be expanded in representations of the SU(2) Bianchi IX isometry group, and the dipole model captures the lowest integer representation of these, connected to hyper-spherical harmonic of angular momentum j=1."

 

[marcus]

Another key paper, which Battisti Marciano cite, is this one by Bianchi Rovelli Vidotto:

http://arxiv.org/abs/1003.3483
Towards Spinfoam Cosmology

Here the authors used a dipole spin network (two nodes connected by four links) to give quantum states of geometry on the (topological) hypersphere S³. They obtained the transition amplitude from one quantum geometric state to another. The treatment breaks away from the earlier LQC homogeneous and isotropic universe.

There are also two earlier papers by Rovelli Vidotto:
On the spinfoam expansion in cosmology. http://arxiv.org/abs/0911.3097
Stepping out of Homogeneity in Loop Quantum Cosmology http://arxiv.org/abs/0805.4585

Incidentally, Battisti Marciano cite two papers in preparation but without giving the titles:
one by themselves and another by Magliaro Marciano Vidotto.

During the past two years Ashtekar's Penn State group has also posted a number of papers on the application of spinfoams to cosmology. The Penn State authors include Ashtekar himself, Henderson, and Wilson-Ewing. Just recently the groups seem to have joined forces and last week we saw a paper by Henderson, Rovelli, Wilson-Ewing and Vidotto:
Local spinfoam expansion in loop quantum cosmology http://arxiv.org/abs/1010.0502

 

[marcus]

The names Battisti and Marciano are new to me so I looked to see any visible background. I think Battisti is/was a PhD student of Giovanni Montani:
http://www.cgwcollaboration.it/webcgm/montani/montani.html
Montani's name is familiar. He is at Rome, has cosmology and quantum gravity among his interests, and is bringing out a book (World Scientific, 2011) called Primordial Cosmology.

Battisti and Marciano list their locations as both Rome (La Sapienza) and Marseille, so maybe they are now postdocs and working in both places. But I only know them to be PhD students. Marciano also seems to be at least parttime at Haverford (where Stephon Alexander, an associate of Ashtekar, has started a QG group.) Things happen fast making it hard to keep track.
Battisti already has 21 papers on arxiv---many before 2009 were co-authored with Montani.

I will see if I can find something about Montani's book on early universe cosmology.
Oh, I see that he is just the principal author, there are 4 co-authors one of which is Battisti.
https://www.amazon.com/dp/9814271004/?tag=pfamazon01-20
We are told the book is "in press" and scheduled to appear March 2011.
We are told that it is 600 pages. That's a lot to prepare for press! I hope they get it out as scheduled!
Here is the Amazon description:
==quote World Scientific publisher's description==
"Primordial Cosmology" deals with one of the most puzzling and fascinating topics debated in modern physics - the nature of the Big Bang singularity. The authors provide a self-consistent and complete treatment of the very early Universe dynamics, passing through a concise discussion of the Standard Cosmological Model, a precise characterization of the role played by the theory of inflation, up to a detailed analysis of the anisotropic and inhomogeneous cosmological models. The most peculiar feature of this book is its uniqueness in treating advanced topics of quantum cosmology with a well-traced link to more canonical and pedagogical notions of fundamental cosmology. This book traces clearly the backward temporal evolution of the Universe, starting with the Robertson-Walker geometry and ending with the recent results of loop quantum cosmology in view of the Big Bounce. The reader is accompanied in this journey by an initial technical presentation which, thanks to the fundamental tools given earlier in the book, never seems heavy or obscure.
==endquote==

 

[atyy]

Interesting statements in http://arxiv.org/abs/0911.3097:

"For this, we need to work with a cosmological model with a sufficient number of degrees of freedom for the relative evolution among variables to be defined."

"The same technique can in principle be applied to other cosmological models with enough degrees of freedom. In particular, the application of the same technique for writing a spinfoam formulation of a Bianchi I cosmology will appear elsewhere."

The elsewhere, unpublished at that time, is the newer paper http://arxiv.org/abs/1010.0502.

So how are the number of degrees of freedom being counted, and what would be too few?

 

[marcus]

Interesting statements in http://arxiv.org/abs/0911.3097:

"For this, we need to work with a cosmological model with a sufficient number of degrees of freedom for the relative evolution among variables to be defined."

"The same technique can in principle be applied to other cosmological models with enough degrees of freedom. In particular, the application of the same technique for writing a spinfoam formulation of a Bianchi I cosmology will appear elsewhere."

The elsewhere, unpublished at that time, is the newer paper http://arxiv.org/abs/1010.0502.

So how are the number of degrees of freedom being counted, and what would be too few?

That's right! I was just about to point that out myself. They changed the title slightly, added Henderson to make 4 co-authors, and introduced locality as a good reason NOT to be dependent on a scalar field to treat as clock. A good reason not to "deparametrize". Rovelli Vidotto followed that approach in the earlier paper.

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

The "too few" degrees of freedom for a relational approach refers to the old LQC where in essence one is limited to a quantized FRW model. In FRW there is only ONE degree of freedom, the scale factor a(t) or "size of the universe" relative to present. So one has to introduce something like a time just to be relational. To have two quantities to relate!

As soon as you move to the DIPOLE situation there are several degrees of freedom, so you can do a relational treatment, without introducing a scalar field gimmick.

What they are saying is in the passage you quoted is simple. The line we want to take (not deparametrizing, not introducing a scalar field to correlate the scalefactor with) requires that the model be just a wee bit more complicated than the old FRW and the old Bojowald LQC----but look! We immediately get this minimal extra complexity by passing to the dipole picture! If you look at it in context you will see that is what they are saying.

 

[marcus]

Atyy, Thanks for pointing out the connection between the earlier Rovelli Vidotto and the Henderson Rovelli Vidotto Wilson-Ewing (HRVW) that just came out this month!

I think that is going to turn out to be a key paper in all this so I'll give the abstract (even though neither Battisti nor Marciano are co-authors).

http://arxiv.org/abs/1010.0502
Local spinfoam expansion in loop quantum cosmology
Adam Henderson, Carlo Rovelli, Francesca Vidotto, Edward Wilson-Ewing
12 pages
(Submitted on 4 Oct 2010)
"The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and Bianchi I models defined by loop quantum cosmology have recently been translated into a spinfoam-like formalism. The construction is facilitated by the presence of a massless scalar field which is used as an internal clock. The implicit integration over the matter variable leads to a nonlocal spinfoam amplitude. In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local."

So they are giving a reason NOT to introduce a matter field to use as clock, when working with spinfoams. That represents a new departure, in one sense, but it was already the approach that Rovelli Vidotto took in the earlier 2009 paper you quoted.

===========================
edit: I neglected to mention that Etera Livine has also co-authored a recent (June 2010) paper in this area. The themes that seem to be coming to light here are spinfoam cosmology, and in particular DIPOLE spinfoam cosmology.

Where the spinfoam chronicles the evolution of a dipole spin network.
http://arXiv.org/abs/1006.2451
Dynamics for a 2-vertex Quantum Gravity Model
Enrique F. Borja, Jacobo Diaz-Polo, Iñaki Garay, Etera R. Livine
28 pages
(Submitted on 12 Jun 2010)
"We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N) invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it."

==quote from Borja Diaz Garay Livine==
Our main source of inspiration for our current approach is the recent model introduced by Rovelli and Vidotto [6]. The logic behind their model is to implement the LQG dynamics on the simplest non-trivial class of spin network states, thus constructing a first order truncation of the full theory. They considered spin network states based on a fixed graph with two vertices related by four edges, so that their model can be called “tetrahedron LQG model”. Very interestingly, it was shown that this model can be understood as reproducing a cosmological setting in LQG and leads to a physical framework very similar to loop quantum cosmology [6, 7]. It was also shown that the same procedure can be successfully applied to the current spinfoam models [8]. This “dipole quantum cosmology” is the starting point of our work.

We consider the generalization of the Rovelli-Vidotto model to spin network states based on a graph with still 2 vertices but now with an arbitrary number N of edges. From their viewpoint, this should allow to introduce more anisotropy/inhomogeneity in their model...
==endquote==

 

[marcus]

The development of Loop cosmology includes some efforts at textbook-level coverage, and popularization.

In less than a month a popular 300-page book called Once Before Time is due out.
https://www.amazon.com/dp/0307272850/?tag=pfamazon01-20
The publisher is Knopf, they expect to have it on sale by November 9.

A 300-page textbook starting from basics and developing the Hamiltonian version of Loop cosmology is scheduled to appear in January 2011:
https://www.amazon.com/gp/product/0521195756/?tag=pfamazon01-20
The publisher is Cambridge Press and the title is Canonical Gravity and Applications.
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521195751

A 600-page textbook called Primordial Cosmology, covering a broader range of topics but including Loop cosmology (probably the spinfoam version that has appeared in the past two years as well as the Hamiltonian, or Canonical version) is supposed to come out in the first half of 2011. The tentative date given is March 2011, but not as firm as the other two since it's listed elsewhere as "spring 2011".
https://www.amazon.com/dp/9814271004/?tag=pfamazon01-20
It is a more ambitious project and involves four authors instead of, as in the other cases mentioned, a single author. The publisher's page shows a photo of the cover and gives more detail about the book:
http://www.worldscibooks.com/physics/7235.html

 

[marcus]

Another book coming out with Bounce Cosmology content is Foundations of Space and
Time. This will have a chapter by Martin Bojowald, who is the author of two books mentioned in the preceding post: Once Before Time, and Canonical Gravity.

Here is the Cambridge University Press page for Foundations:
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521114400
Our thread on the book:
https://www.physicsforums.com/showthread.php?t=427475

I guess there are two points to make:
1. Bounce cosmology is entering mainstream---many researchers, beginnings of phenomenology (things to look for in the CMB as more observational data becomes available), many well-cited papers, and now the expected appearance of textbooks, professional-level books, and popularizations.

2. Bounce cosmology is fairly robust---it appears in a variety of quantum cosmology models, including the spinfoam dynamics of the full LQG theory, including versions where symmetry/uniformity assumptions have been relaxed, where inflation is included, and so forth.