Loop Quantum Cosmology has so far deal mainly with highly uniform models like what is normally studied in classical cosmology---homogeneous and isotropic universes.(adsbygoogle = window.adsbygoogle || []).push({});

But in the past couple of years several papers have appeared that relax the uniformity assumptions---they get into studying universes that are NOT homogeneous and isotropic.

The same has happened in LQG black hole research---people have started studying asymmetric collapse, and asymmetric bounce. The singularity is eliminated as usual but anisotropic models can give you different results. I don't want to get into a discussion of LQG black hole research. Just mention it in passing.

Have to go now, when I get back I will get some links to LQC papers that treat inhomog and anistropic cases.

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Back now. By coincidence what I think is one of the most interesting relaxed-uniformity Loop Cosmo papers is co-authored by Francesca Vidotto who used to post here a lot and still comes by sporadically. I think her first real contact with LQG was when she attended the QG School at Zakopane in March 2007. The ski was still good so in the morning they had tutorials on covariant LQG, canonical LQG, Triangulations QG, Asymptotic Safety, and in the afternoon they went skiing. Zakopane is a resort in the Polish mountains. So in a sense this paper began there:

http://arxiv.org/abs/0805.4585

Stepping out of Homogeneity in Loop Quantum Cosmology

Carlo Rovelli, Francesca Vidotto

Classical and Quantum Gravity 25:225024,2008

16 pages

(Submitted on 29 May 2008)

"We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation."

Today we saw on arxiv the follow-up to Rovelli-Vidotto

http://arxiv.org/abs/0911.2653

Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations

Marco Valerio Battisti, Antonino Marciano, Carlo Rovelli

21 pages

(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."

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To provide a little background, there areclassicallop-sided, irregular versions of the big crunch or big bang, in which (for example) things collapse/expand at different rates in different directions. These irregular classical solutions are described using terms like Bianchi I, Bianchi IX, Kasner, and Taub. The Bianchi series classifies partially restricted symmetries of space. Kasner and Taub are classical solutions of the GR equation with reduced symmetry that can lead to seemingly chaotic highly complicated singularities, one being the socalled "Mixmaster".

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# LQC into irregular cosmo

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