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http://arxiv.org/abs/1010.1258

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

http://arxiv.org/abs/0911.2653

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."

**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."

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