The effect of inhomogeneous expansion on the supernova observations

We consider an inhomogeneous but spherically symmetric Lemaitre Tolman - Bondi model to demonstrate that spatial variations of the expansion rate can have a significant effect on the cosmological supernova observations. A model with no dark energy but a local Hubble parameter about 15% larger than its global value fits the supernova data better than the homogeneous model with the cosmological constant. The goodness of the fit is not sensitive to inhomogeneities in the present-day matter density, and our best fit model has Omega(M)( r) similar to 0.3, in agreement with galaxy surveys. We also compute the averaged expansion rate, defined by the Buchert equations, of the best fit model and show explicitly that there is no average acceleration.