Vertex Expansion for the Bianchi I model

Abstract

A perturbative expansion of Loop Quantum Cosmological transitions amplitudes of Bianchi I models is performed. Following the procedure outlined in [1,2] for isotropic models, it is shown that the resulting expansion can be written in the form of a series of amplitudes each with a fixed number of transitions mimicking a spin foam expansion. This analogy is more complete than in the isotropic case, since there are now the additional anisotropic degrees of freedom which play the role of `colouring' of the spin foams. Furthermore, the isotropic expansion is recovered by integrating out the anisotropies.

15 pages, 2 figures

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• Cosmological constant in spinfoam cosmology
• Many-nodes/many-links spinfoam: the homogeneous and isotropic case
• Loop Quantum Gravity
• Local spinfoam expansion in loop quantum cosmology
• Spin-foam model for gravity coupled to massless scalar field
• Symmetry Reduced Loop Quantum Gravity: A Bird's Eye View
• Diffeomorphism invariant cosmological sector in loop quantum gravity
• The new spin foam models and quantum gravity
• Path Integral of Bianchi I models in Loop Quantum Cosmology
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects