Abstract
We quantize a perturbed Friedmann–Lemaître–Robertson–Walker model coupled to a massive scalar field. We consider only scalar perturbations, in a universe whose spatial sections have the topology of a three-sphere. The local gauge freedom is fixed at the classical level. We choose a preferred parametrization of the system by adapting uniqueness criteria for the quantization of scalar fields with time-dependent mass. The Hilbert space of the theory is constructed combining a polymer representation for the homogeneous background and the preferred Fock quantization for the perturbations. Finally, we propose a prescription to promote the Hamiltonian constraint to a quantum operator, and characterize the states annihilated by it in terms of their initial data at the minimum-volume section.
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Acknowledgement
This work was supported by the research grant MICINN/MINECO FIS2011-30145-C03-02 from Spain.
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Fernández-Méndez, M., Marugán, G.A.M., Olmedo, J. (2014). Complete Quantization of Scalar Cosmological Perturbations. In: García-Parrado, A., Mena, F., Moura, F., Vaz, E. (eds) Progress in Mathematical Relativity, Gravitation and Cosmology. Springer Proceedings in Mathematics & Statistics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40157-2_35
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DOI: https://doi.org/10.1007/978-3-642-40157-2_35
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