  The existence of stars and galaxies reqires cosmological models with an
inhomogeneous matter and radiation distribution. But in these models the
initial singularity surface t_0(r) is in general homogeneous (independent of
r). In this second paper of a series devoted to an inhomogeneous Big Bang
singularity, we investigate the cosmic microwave background radiation (CMBR)
dipole. A special Tolman-Bondi Universe is used to study the effect of a
Big-Bang singularity, depending linearly on r, on the CMBR anisotropy. It is
shown that, for an observer located off the ``center'' of this Universe (r=0),
the parameters of the model can be tuned so as to reproduce, with a good
approximation, the dipole and the quadrupole moments of the CMBR anisotropy
observed in recent experiments. If the dipole should prove cosmological, a
slight delaying of the Big-Bang over spatial coordinates would thus be a good
candidate for its interpretation.
