The clustering of critical points in the evolving cosmic web. Issue 3 (9th February 2021) - Shim, J; Codis, S; Pichon, C; Pogosyan, D; Cadiou, C
ABSTRACT: Focusing on both small separations and baryonic acoustic oscillation scales, the cosmic evolution of the clustering properties of peak, void, wall, and filament-type critical points is measured using two-point correlation functions in ΛCDM dark matter simulations as a function of their relative rarity. A qualitative comparison to the corresponding theory for Gaussian random fields allows us to understand the following observed features: (i) the appearance of an exclusion zone at small separation, whose size depends both on rarity and signature (i.e. the number of negative eigenvalues) of the critical points involved; (ii) the amplification of the baryonic acoustic oscillation bump with rarity and its reversal for cross-correlations involving negatively biased critical points; (iii) the orientation-dependent small-separation divergence of the cross-correlations of peaks and filaments (respectively voids and walls) that reflects the relative loci of such points in the filament's (respectively wall's) eigenframe. The (cross-) correlations involving the most non-linear critical points (peaks, voids) display significant variation with redshift, while those involving less non-linear critical points seem mostly insensitive to redshift evolution, which should prove advantageous to model. The ratios of distances to the maxima of the peak-to-wall and peak-to-void over that of the peak-to-filament cross-correlation are ${\sim} \sqrt{2}$ and ${\sim} \sqrt{3}$, respectively, which could be interpreted as the cosmic crystal being on average close to a cubic lattice. The insensitivity to redshift evolution suggests that the absolute and relative clustering of critical points could become a topologically robust alternative to standard clustering techniques when analysing upcoming surveys such as Euclid or Large Synoptic Survey Telescope (LSST).