An inhomogeneous universe with thick shells and without cosmological
  constant
  We build an exact inhomogeneous universe composed of a central flat Friedmann
zone up to a small redshift $z_1$, a thick shell made of anisotropic matter, an
hyperbolic Friedmann metric up to the scale where dimming galaxies are observed
($z\simeq 1.7$) that can be matched to a hyperbolic Lema\^{i}tre-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.
