Can the Stephani model be an alternative to FRW accelerating models?
  A class of Stephani cosmological models as a prototype of non-homogeneous universe is considered. The non-homogeneity can lead to accelerated evolution which is now observed from the SNIa data. Three samples of type Ia supernovae obtained by Perlmutter at al., Tonry et al. and Knop et al. are taken into account. Different statistical methods (best fits as well as maximum likelihood method) to obtain estimates of the model parameters are used. Stephani model is considered as an alternative to the concordance of Lambda-CDM model in the explanation of the present acceleration of the universe. The model explains the acceleration of the universe at the same level of accuracy as the Lambda-CDM model. From the best fit analysis it follows that the Stephani model is characterized by higher value of nonrelativistic matter density parameter than the Lambda-CDM model. It is also shown that the obtained results are consistent with location of CMB peaks. 
Wlodzimierz Godlowski, Jerzy Stelmach, Marek Szydlowski