Generalized Hubble law, violation of the cosmological principle and   Supernovae
  The acceleration of the cosmic expansion has been discovered as a consequence of redshift Supernovae data. In the usual way, this cosmic acceleration is explained by the presence of a positive cosmological constant or quantum vacuum energy, in the background of standard Friedmann models. Recently, looking for an alternative explanation, I have considered an inhomogeneous barotropic spherically symmetric spacetime. Obviously, in this inhomogeneous model the philosophical cosmological principle is not verified. Within this framework, the kinematical acceleration of the cosmic fluid or, equivalently, the inhomogeneity of matter, is just the responsible of the SNe Ia measured cosmic acceleration. Moreover, this model gives rise to a generalized Hubble law with two anisotropic terms (dipole acceleration and quadrupole shear), besides the expansion one. The dipole term of this generalized Hubble law could explain, in a cosmological setting, the observed large scale flow of matter, without to have recourse to peculiar velocity-type newtonian models which assume a Doppler dipole. 
J.-F. Pascual-S\'anchez