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. Yet, the test assumes the universe and the distribution of supernovae to be statistically homogeneous and isotropic. Since the first version of the test is troubled by systematic effects, we modify the analysis to be independent of the calibration of the supernova absolute magnitude. As a result, all systematics are reduced. While most supernova data sets provide evidence for acceleration, when the test is applied, the SDSS data set lacks this evidence.

Due to structure in the universe, the assumption of homogeneity and isotropy might not be justified - especially on small scales. As the Einstein equations are non-linear, spatial averaging and temporal evolution do not commute. Consequently, a universe with structure evolves differently than a perfectly homogeneous universe. The size of this backreaction effect is, however, discussed very controversially. In this work, we test the influence of backreaction on the measurement of the present Hubble rate using supernova data. We find, however, no evidence for backreaction in the presently available supernova data sets.