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We introduce scalar perturbations in a homogeneous and isotropic universe with compact spatial sections filled with a massive scalar field. The gauge freedom is then almost entirely removed by imposing two different sets of gauge-fixing conditions, which lead to consistent results. We quantize completely the model by combining a polymer representation for the homogeneous degrees of freedom and a Fock representation for the perturbations. Criteria of symmetry and unitary dynamics determine the latter uniquely. We also present an equivalent quantization in terms of gauge-invariant variables. Moreover, we propose a quantum implementation of the Hamiltonian constraint whose solutions are totally characterized by their initial value on the minimum-volume section.

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Mikel Fernández Méndez, Instituto de Estructura de la Materia, CSIC, Madrid
Seminarraum Theoretische Physik
Contact: not specified