Martin- Benito, M.Garay Elizondo, Luis JavierMena Marugán, Guillermo A.2023-06-202023-06-202011[1] Bojowald M 2008 Living Rev. Rel. 11 4 [2] Gowdy R H 1974 Ann. Phys. 83 203 [3] Martín-Benito M, Garay L J and Mena Marug´an G A 2008 Phys. Rev. D 78 083516 [4] Mena Marugán G A and Martín-Benito M 2009 Int. J. Mod. Phys. A 24 2820 [5] Martín-Benito M, Mena Marugán G A and Paw lowski T 2008 Phys. Rev. D 78 064008 [6] Ashtekar A and Wilson-Ewing E 2009 Phys. Rev. D 79 083535 [7] Garay L J, Martín-Benito M and Mena Marugán G A 2010 Phys. Rev. D 82 044048 [8] Martín-Benito M, Mena Marugán G A and Wilson-Ewing E 2010 Phys. Rev. D 82 084012 [9] Corichi A, Cortez J and Mena Marugán G A 2006 Phys. Rev. D 73 084020 [10] Corichi A, Cortez J, Mena Marug´an G A and Velhinho J M 2006 Classical Quantum Gravity 23 6301 [11] Cortez J, Mena Marugán G A and Velhinho J M 2007 Phys. Rev. D 75 0840271742-658810.1088/1742-6596/314/1/012047https://hdl.handle.net/20.500.14352/44524© IOP Publishing Ltd. This work was in part supported by the Spanish MICINN Project No. FIS2008-06078-C03-03 and the Consolider-Ingenio Program CPAN No. CSD2007-00042. M. M-B has been supported by CSIC and the European Social Fund under the grant I3P-BPD2006. Spanish Relativity Meeting (ERE 2010) on Gravity as a Crossroad in Physics (2010. Granada, España)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.engjournal articlehttp://dx.doi.org/10.1088/1742-6596/314/1/012047http://iopscience.iop.org/http://arxiv.org/pdf/1012.3713v1.pdfopen access51-73Astronomy & AstrophysicsPhysicsmultidisciplinaryparticles & fieldsFísica-Modelos matemáticosFísica matemática