Minkowski functionals and the nonlinear perturbation theory in the largescale structure: secondorder effects
Abstract
The secondorder formula of Minkowski functionals in weakly nonGaussian fields is compared with the numerical $N$body simulations. Recently, weakly nonGaussian formula of Minkowski functionals is extended to include the secondorder effects of nonGaussianity in general dimensions. We apply this formula to the threedimensional density field in the largescale structure of the Universe. The parameters of the secondorder formula include several kinds of skewness and kurtosis parameters. We apply the treelevel nonlinear perturbation theory to estimate these parameters. First we compare the theoretical values with those of numerical simulations on the basis of parameter values, and next we test the performance of the analytic formula combined with the perturbation theory. The secondorder formula outperforms the firstorder formula in general. The performance of the perturbation theory depends on the smoothing radius applied in defining the Minkowski functionals. The quantitative comparisons are presented in detail.
 Publication:

arXiv eprints
 Pub Date:
 November 2020
 DOI:
 10.48550/arXiv.2012.00203
 arXiv:
 arXiv:2012.00203
 Bibcode:
 2020arXiv201200203M
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 12 pages, 7 figures, 1 table