Direction Dependence in Supernova Data: Constraining Isotropy

Abstract

We revise and extend the extreme value statistic, introduced in \cite{gup08}, to study directional dependence in the high redshift supernova data; arising either from departures from the cosmological principle or due to direction dependent statistical systematics in e data. We introduce a likelihood function that analytically marginalises over the Hubble constant, and use it to extend our previous statistic. We also introduce a new statistic that is sensitive to direction dependence arising from living off-centre inside a large void, as well as previously mentioned reasons for anisotropy. We show that for large data sets this statistic has a limiting form that can be computed analytically. We apply our statistics to the gold data sets from \cite{rie04} and \cite{rie07}, as in our previous work. Our revision and extension of previous statistic shows that 1) the effect of marginalsing over Hubble constant instead of using its best fit value has only a marginal effect on our results. However, correction of errors in our previous work reduce the level of non-Gaussianity in the 2004 gold data that was found in our earlier work. The revised results for the 2007 gold data show that the data is consistent with isotropy and Gaussianity. Our second statistic confirms these results.