Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: We develop the -triangulated- version of loop quantum cosmology, recentlyintroduced in the literature. We focus on the -dipole- cosmology, where spaceis a three-sphere and the triangulation is formed by two tetrahedra. We showthat the discrete fiducial connection has a simple and appealing geometricalinterpretation and we correct the ansatz on the relation between the modelvariables and the Friedmann-Robertson-Walker scale factor. The modified ansatzleads to the convergence of the Hamiltonian constraint to the continuum one. Wethen ask which degrees of freedom are captured by this model. We show that themodel is rich enough to describe the anisotropic Bianchi IX Universe, andgive the explicit relation between the Bianchi IX variables and the variablesof the model. We discuss the possibility of using this path in order to definethe quantization of the Bianchi IX Universe. The model contains more degrees offreedom than Bianchi IX, and therefore captures some inhomogeneous degrees offreedom as well. Inhomogeneous degrees of freedom can be expanded inrepresentations of the SU2 Bianchi IX isometry group, and the dipole modelcaptures the lowest integer representation of these, connected tohyper-spherical harmonic of angular momentum j=1.



Author: Marco Valerio Battisti, Antonino Marciano, Carlo Rovelli

Source: https://arxiv.org/



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