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 important to 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 the family of Minkowski Functionals. We introduce a new code, suitable for the analysis of large data sets without smoothing and without the construction of excursion sets. We provide new tools to measure correlation properties, putting emphasis on explicitly 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 find significant deviations from the Λ cold dark matter mock catalogues on samples as large as 500 h − 1 Mpc (more than 3σ) and slight deviations of around 2σ on 700 h − 1 Mpc, and we investigate possible sources of these deviations.