We discuss the possibility of identifying anisotropic and/or inhomogeneous cosmological models using type Ia supernova data. A search for correlations in current type Ia peak magnitudes over a large range of angular scales yields a null result. However, the same analysis limited to supernovae at low redshift shows a feeble anticorrelation at the 2σ level at angular scales θ≈40°. Upcoming data from, e.g., the SNLS (Supernova Legacy Survey) and the SDSS-II (SDSS: Sloan Digital Sky Survey) supernova searches will improve our limits on the size of—or possibly detect—possible correlations also at high redshift at the per cent level in the near future. With data from the proposed SNAP (SuperNova Acceleration Probe) satellite, we will be able to detect the induced correlations from gravitational lensing on type Ia peak magnitudes on scales less than a degree.

We use the new Type Ia supernovae discovered by the Sloan Digital Sky Survey-II supernova survey, together with additional supernova data sets as well as observations of the cosmic microwave background and baryon acoustic oscillations to constrain cosmological models. This complements the standard cosmology analysis presented by Kessler et al. in that we discuss and rank a number of the most popular nonstandard cosmology scenarios. When this combined data set is analyzed using the MLCS2k2 light-curve fitter, we find that more exotic models for cosmic acceleration provide a better fit to the data than the ΛCDM model. For example, the flat Dvali-Gabadadze-Porrati model is ranked higher by our information-criteria (IC) tests than the standard model with a flat universe and a cosmological constant. When the supernova data set is instead analyzed using the SALT-II light-curve fitter, the standard cosmological-constant model fares best. This investigation of how sensitive cosmological model selection is to assumptions about, and within, the light-curve fitters thereby highlights the need for an improved understanding of these unresolved systematic effects. Our investigation also includes inhomogeneous Lemaître-Tolman-Bondi (LTB) models. While our LTB models can be made to fit the supernova data as well as any other model, the extra parameters they require are not supported by our IC analysis. Finally, we explore more model-independent ways to investigate the cosmic expansion based on this new data set.

Inhomogeneous universe models have been proposed as an alternative explanation for the apparent acceleration of the cosmic expansion that does not require dark energy. In the simplest class of inhomogeneous models, we live within a large, spherically symmetric void. Several studies have shown that such a model can be made consistent with many observations, in particular the redshift-luminosity distance relation for type Ia supernovae, provided that the void is of Gpc size and that we live close to the center. Such a scenario challenges the Copernican principle that we do not occupy a special place in the universe. We use the first-year Sloan Digital Sky Survey-II supernova search data set as well as the Constitution supernova data set to put constraints on the observer position in void models, using the fact that off-center observers will observe an anisotropic universe. We first show that a spherically symmetric void can give good fits to the supernova data for an on-center observer, but that the two data sets prefer very different voids. We then continue to show that the observer can be displaced at least fifteen percent of the void scale radius from the center and still give an acceptable fit to the supernova data. When combined with the observed dipole anisotropy of the cosmic microwave background however, we find that the data compells the observer to be located within about one percent of the void scale radius. Based on these results, we conclude that considerable fine-tuning of our position within the void is needed tofit the supernova data, strongly disfavouring the model from a Copernican principle point of view.

We investigate constraints on dark energy fluctuations using type Ia supernovae. If dark energy is not in the form of a cosmological constant, that is if the equation of state is not equal to -1, we expect not only temporal, but also spatial variations in the energy density. Such fluctuations would cause local variations in the universal expansion rate and directional dependences in the redshift-distance relation. We present a scheme for relating a power spectrum of dark energy fluctuations to an angular covariance function of standard candle magnitude fluctuations. The predictions for a phenomenological model of dark energy fluctuations are compared to observational data in the form of the measured angular covariance of Hubble diagram magnitude residuals for type Ia supernovae in the Union2 compilation. The observational result is consistent with zero dark energy fluctuations. However, due to the limitations in statistics, current data still allow for quite general dark energy fluctuations as long as they are in the linear regime.