MG13 - Talk detail

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The quantization of cosmological systems by using loop quantum cosmology techniques includes the consideration of the so-called improved dynamics in order to obtain successful results. However, the application of the improved dynamics prescription for anisotropic cosmologies leads to a quite involved Hamiltonian constraint operator. Consequently, in order to solve the system, it is necessary to introduce some approximations to obtain a treatable quantum constraint. Considering first the loop quantized Bianchi I model with local rotational symmetry (LRS), we introduce a controlled approximation to the anisotropy term that allows us to obtain approximated solutions to the quantum Hamiltonian constraint. Then we use this approximation in the hybrid quantized LRS-Gowdy model with three-torus topology and minimally coupled to a massless scalar field. This system can be seen as matter and gravitational inhomogeneities, that are quantized à la Fock, propagating on a loop quantized LRS-Bianchi I background. By using this approximation we are able to obtain a physically interesting family of approximated quantum solutions.

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