Quantum Gowdy Model within the new LQC Improved Dynamics

L.J. Garay, M. Martín-Benito, G.A. Mena Marugán

The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology allowing the presence of inhomogeneities. We analyze the particular case of the linearly polarized Gowdy T³ model. This system can be regarded as a compact Bianchi I cosmology which allows inhomogeneous modes to travel in one direction. We detail a hybrid quantum theory in which we combine the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward recently by Ashtekar and Wilson-Ewing, with a Fock quantization of the inhomogeneities. In doing that we address several issues like the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, and the representation of the Hamiltonian constraint. We argue that this constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe with a well posed
initial value problem: physical solutions are completely determined by the data on an initial section of constant Bianchi I volume. 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.