Direct Minkowski Functional analysis of large redshift surveys: a new high--speed code tested on the luminous red galaxy Sloan Digital Sky Survey-DR7 catalogue

As deeper galaxy catalogues are soon to come, it becomes even more importantto measure large-scale fluctuations in the catalogues with robust statistics that cover all moments of the galaxy distribution.In this paper we reinforce a direct analysis of galaxy data by employing the Germ-Grain method to calculate thefamily of Minkowski Functionals. We introduce a new code, suitable for the analysis of large data sets without smoothingand without the construction of excursion sets. We provide new tools to measure correlation properties, putting emphasis onexplicitly isolating non-Gaussian correlations with the help of integral-geometric relations. As a first application we present the analysis of large-scale fluctuations in the luminous red galaxy sample of Sloan Digital Sky Survey data release 7 data. We findsignificant deviations from the $\Lambda$ cold dark matter mock catalogues on samples as large as $500h^{-1}$Mpc (more than $3\sigma$)and slight deviations of around $2\sigma$ on $700h^{-1}$Mpc, and we investigate possible sources of these deviations.