Testing spherical evolution for modelling void abundances

Abstract

We compare analytical predictions of void volume functions to those measured from Nbody simulations, detecting voids with the zobov void finder. We push to very small, nonlinear voids, below few h −1 .Mpc radius, by considering the unsampled DM density field. We also study the case where voids are identified using halos. We develop analytical formula for the void abundance of both the excursion set approach and the peaks formalism. These formula are valid for random walks smoothed with a top-hat filter in real space, with a large class of realistic barrier models. We test the extent to which the spherical evolution approximation, which forms the basis of the analytical predictions, models the highly aspherical voids that occur in the cosmic web, and are found by a watershed-based algorithm such as zobov. We show that the volume function returned by zobov is quite sensitive to the choice of treatment of sub-voids, a fact that has not been appreciated previously. For reasonable choices of sub-void exclusion, we find that the Lagrangian density δ v of the zobov voids -which is predicted to be a constant δ v ≈ −2.7 in the spherical evolution model -is different from the predicted value, showing substantial scatter and scale dependence. This result applies to voids identified at z = 0 with effective radius between 1 and 10M pc.h −1 . Our analytical approximations are flexible enough to give a good description of the resulting volume function; however, this happens for choices of parameter values that are different from those suggested by the spherical evolution assumption. We conclude that analytical models for voids must move away from the spherical approximation in order to be applied successfully to observations, and we discuss some possible ways forward.

Cluster–void Degeneracy Breaking: Dark Energy, Planck, and the Largest Cluster and Void

“…The observation is defined in real space, which introduces non-Markovian corrections. Achitouv et al (2015) derive a "DDB" void MF including such corrections, and stochasticity in the void formation barrier. We have computed that these corrections give an ∼10% increase in the void MF compared to SvdW for rescaled to the survey patch, and extreme-void statistics in the largest N-body simulations (e.g., Hotchkiss et al 2015).…”

Testing the imprint of nonstandard cosmologies on void profiles using Monte Carlo random walks

“…However, the spherical criterion is a deterministic prediction that can not encapsulate all of the non-linear interactions of the density fluctuations. For instance in [14], the authors have measured, from an N-body simulation, the extrapolated linear density contrasts that lead to the voids identified with ZOBOV [37]. They show that on average and for large voids, the critical density was consistent with the spherical prediction of ∆ ∼ −2.7 but showing a nonnegligible scatter around this mean value.…”

“…This value is often used in the excursion set theory (e.g. [14,29,44]) to predict the abundance of voids, (when a random linear trajectory crosses that threshold at the largest smoothing scale without crossing the linear threshold of halo formation). One may be tempted to establish a link between the log-normal random walks that are identified as voids and the corresponding linear trajectories.…”

“…[13]), measuring their abundance or their density profiles (e.g. [1,[14][15][16]) or looking at the clustering of matter in underdense environments [17,18].…”

“…[4,5,27,28]). This definition is very helpful when trying to link the theory of an expanding underdense patch to the prediction of void abundance (for instance [14,29]). Other techniques based on watershed transforms or dynamical properties around voids (e.g.…”