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General Relativity and Quantum Cosmology, gr-qc
Abstract:
The linearly polarized Gowdy $T^3$ model can be regarded as compact Bianchi I
cosmologies with inhomogeneous modes allowed to travel in one direction. We
study a hybrid quantization of this model that combines the loop quantization
of the Bianchi I background, adopting the improved dynamics scheme put forward
by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities.
The Hamiltonian constraint operator provides a resolution of the cosmological
singularity and superselects separable sectors. We analyze the complicated
structure of these sectors. In any of them the Hamiltonian constraint provides
an evolution equation with respect to the volume of the associated Bianchi I
universe, with a well posed initial value problem. This fact allows us to
construct the Hilbert space of physical states and to show that we recover the
standard quantum field theory for the inhomogeneities.
