Dark energy or apparent acceleration due to a relativistic cosmological model more complex than the Friedmann-Lemaitre-Robertson-Walker model?

We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data almost as well as the Lambda-CDM model without requiring a dark energy component. The Szekeres models were originally derived as an exact solution to Einstein's equations with a general metric that has no symmetries, and they are regarded as good candidates to model the true lumpy universe that we observe. The null geodesics in these models are not radial. The best fit model found is also consistent with the requirement of spatial flatness at cosmic microwave background scales. The first results presented here seem to encourage further investigations of apparent acceleration using various inhomogeneous models, and other constraints from cosmic microwave background and large structure need to be explored next.