Abstract
ABSTRACT Minkowski functionals (MFs) are a set of statistics that characterize the geometry and topology of the cosmic density field and contain complementary information to the standard two-point analyses. We present medusa, an implementation of an accurate method for estimating the MFs of three-dimensional point distributions. These estimates are inferred from triangulated isodensity surfaces that are constructed from the Delaunay tessellation of the input point sample. medusa can account for periodic boundary conditions, which is crucial for the analysis of N-body simulations. We validate our code against several test samples with known MFs, including Gaussian random fields with a ΛCDM power spectrum, and find excellent agreement with the theory predictions. We use medusa to measure the MFs of synthetic galaxy catalogues constructed from N-body simulations. Our results show clearly non-Gaussian signatures that arise from the non-linear gravitational evolution of the density field. We find that, although redshift-space distortions change our MFs estimates, their impact is considerably reduced if these measurements are expressed as a function of the volume-filling fraction. We also show that the effect of Alcock–Paczynski (AP) distortions on the MFs can be described by scaling them with different powers of the isotropic AP parameter q defined in terms of the volume-averaged distance DV(z). Thus the MFs estimates by medusa are useful probes of non-linearities in the density field, and the expansion and growth of structure histories of the Universe.
Highlights
The analysis of the large-scale distribution of galaxies by means of two-point statistics, such as the correlation function or the power spectrum, has played a key role in establishing the current ΛCDM cosmological paradigm (Davis & Peebles 1983; Efstathiou et al 2002; Tegmark et al 2004; Cole et al 2005; Eisenstein et al 2005; Blake et al 2011; Sánchez et al 2006, 2017; Alam et al 2017a; eBOSS Collaboration et al 2020)
We focus on the full set of Minkowski functionals (MFs), introduced to large-scale structure (LSS) studies by Mecke et al (1994) to describe the geometry and topology of the cosmic density field
We focus on three main issues of great importance for the analysis of the MFs of triangulated surfaces inferred from real galaxy surveys: non-Gaussian features due to non-linear gravitational evolution, redshift-space distortions (RSD), and Alcock-Paczynski (AP) distortions
Summary
The analysis of the large-scale distribution of galaxies by means of two-point statistics, such as the correlation function or the power spectrum, has played a key role in establishing the current ΛCDM cosmological paradigm (Davis & Peebles 1983; Efstathiou et al 2002; Tegmark et al 2004; Cole et al 2005; Eisenstein et al 2005; Blake et al 2011; Sánchez et al 2006, 2017; Alam et al 2017a; eBOSS Collaboration et al 2020). Present-day surveys allow for accurate measurements of the threepoint correlation function and the bispectrum (Marín et al 2013; Gil-Marín et al 2015; Gil-Marín et al 2017; Slepian et al 2017a,b; Pearson & Samushia 2018). These analyses are challenging due to the complexity associated with the measurement of all possible combinations of triplets, their corresponding theoretical modelling, and the estimation of accurate covariance matrices. The analysis of higher order N-point functions is at the moment infeasible
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