An inhomogeneous universe with thick shells and without cosmological constant

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We build an exact inhomogeneous universe composed of a central flat Friedmann zone up to a small redshift z₁, a thick shell made of anisotropic matter, an hyperbolic Friedmann metric up to the scale where dimming galaxies are observed (z≃ 1.7) that can be matched to a hyperbolic Lemaître-Tolman-Bondi spacetime to best fit the WMAP data at early epochs. We construct a general framework which permits us to consider a non-uniform clock rate for the universe. As a result, both for a uniform time and a uniform Hubble flow, the deceleration parameter extrapolated by the central observer is always positive. Nevertheless, by taking a non-uniform Hubble flow, it is possible to obtain a negative central deceleration parameter, that, with certain parameter choices, can be made the one observed currently. Finally, it is conjectured a possible physical mechanism to justify a non-uniform time flow.