Cosmic expansion in homogeneous and inhomogeneous universes : supernovae type Ia as cosmic probes Since it has been discovered in the late 1990s that the universe is likely to be expanding accelerated a large variety of cosmological models have been developed that allow for cosmic acceleration. Some of the models include a dark energy term that causes the acceleration while others modify gravity or drop the assumption of homogeneity and isotropy. As an example of such a model we analyze a braneworld model with one timelike extra dimension. There are strong constraints to the parameter values of such a model resulting from the claim that there must be a physical solution to the Friedmann equation at least between now and the time of recombination. We fit the model to supernova type Ia data and check the consistency of the result with other observations. For parameter values that are consistent with observations the braneworld model is indistinguishable from a [Lambda]CDM universe as far as the considered cosmological tests are concerned. Although all cosmological models that assume homogeneity and isotropy of the universe and have been tested so far conclude that the universe expands accelerated this does not prove acceleration beyond doubt. Therefore we constructed a test of acceleration which is model independent in the sense that no assumptions about the content of the universe or about the parameterization of the deceleration parameter are made and that it does not assume any dynamical equations of motion...