Abstract
A multiresolution analysis was performed to estimate the large-scale structure of cosmological $N$-body simulations. To explore relations between the multiresolution analysis and the galaxy distributions, a method that is familiar to image processing engineering was utilized. We proposed a new technique for quantifying the large-scale structures, and found that this is useful to discriminate differences in galaxy distributions among power-law simulations. We next applied the multiresolution analysis to CDM simulations, and also obtained a confirmation of the usefulness of this analysis; our new technique had advantages in clearly distinguishing differences in galaxy distributions in CDM models. We finally compared the galaxy distributions in the two-dimensional observational data (LEDA2 d subsample) with those in CDM mock samples, and found that the standard CDM model does not reproduce the galaxy distributions in our universe.
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