We develop approximation methods in the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field, for the case of threetorus spatial topology. The loop quantization of the homogeneous gravitational sector of the Gowdy model (according to the improved dynamics prescription) and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical results calls for the introduction of well justified approximations. We first show how to approximate the homogeneous part of the Hamiltonian constraint, corresponding to Bianchi I geometries, as if it described a Friedmann-Robertson-Walker (FRW) model corrected with anisotropies. This approximation is valid in the sector of high energies of the FRW geometry (concerning its contribution to the constraint) and for anisotropy profiles that are sufficiently smooth. In addition, for certain families of states related to regimes of physical interest, with negligible quantum effects of the anisotropies and small inhomogeneities, one can approximate the Hamiltonian constraint of the inhomogeneous system by that of an FRW geometry with a relatively simple matter content, and then obtain its solutions.

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Objective: Neuroimaging studies in children with ADHD indicate that their brain exhibits an atypical functional connectivity pattern characterized by increased local connectivity and decreased distant connectivity. We aim to evaluate if the local and distant distribution of functional connectivity is also altered in adult samples with ADHD who have never received medication before. Methods: We compared local and distant functional connectivity between 31 medication-naïve adults with ADHD and 31 healthy controls and tested whether this pattern was associated with symptoms severity scores. Results: ADHD sample showed increased local connectivity in the dACC and the SFG and decreased local connectivity in the PCC. Conclusion: Results parallel those obtained in children samples suggesting a deficient integration within the DMN and segregation between DMN, FPN, and VAN. These results are consistent with the three main frameworks that explain ADHD: the neurodevelopmental delay hypothesis, the DMN interference hypothesis and multi-network models.

Abstract. We study the hybrid quantization of the linearly polarized Gowdy T 3 model with a massless scalar field with the same symmetries as the metric. For simplicity, we quantize its restriction to the model with local rotational symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the geometry are quantized à la loop, leading to the resolution of the cosmological singularity. A Fock quantization is employed both for the matter and the gravitational inhomogeneities. Owing to the inclusion of the massless scalar field this system allows us to modelize flat FriedmannRobertson-Walker cosmologies filled with inhomogeneities propagating in one direction, providing a perfect scenario to study the quantum back-reaction of the inhomogeneities on the polymeric homogeneous and isotropic background.

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