The most detailed constraints on the accelerating expansion of the universe and the nature of dark energy are derived from the high-redshift supernova data, assuming that the luminosity distance versus redshift relation is isotropic and the errors in the measurements are Gaussian. There is a possibility that there is a systematic direction dependence in the data, either due to uncorrected, known physical processes or because there are tiny departures from the cosmological principle, making the universe slightly anisotropic. To investigate this possibility, we introduce a statistic based on extreme value theory and apply it to the gold data sets from Riess et al. Our analysis indicate a systematic, directional dependence in the supernova data in both sets, which using the bootstrap distribution comes to about 80 per cent level of confidence for Riess et al. and 90 per cent for Riess et al. Equally importantly, we show that while the 2007 data fit Λ cold dark matter (ΛCDM) model better than the 2004 data, the level of non-Gaussianity, quantified by departures of our statistic from the Gaussian predictions has become worse. In fact, we find that Riess et al. data lie totally outside the distribution obtained by assuming the noise to be Gaussian.
Gupta, S., Saini, T. D., & Laskar, T. (2008). Direction dependence and non-Gaussianity in the high-redshift supernova data. Monthly Notices of the Royal Astronomical Society, 388(1), 242-246. https://doi.org/10.1111/j.1365-2966.2008.13377.x