Warm dark matter (WDM) has been proposed as an alternative to cold dark matter (CDM), to resolve issues such as the apparent lack of satellites around the Milky Way. Even if WDM is not the answer to observational issues, it is essential to constrain
the nature of the dark matter. The effect of WDM on haloes has been extensively studied, but the small-scale initial smoothing in WDM also affects the present-day cosmic web and voids. It suppresses the cosmic sub-web inside voids, and the formation of both void haloes and subvoids. In $N$-body simulations run with different assumed WDM masses, we identify voids with the ZOBOV algorithm, and cosmic-web components with the ORIGAMI algorithm. As dark-matter warmth increases (i.e., particle mass decreases), void density minima grow shallower, while void edges change little. Also, the number of subvoids decreases. The density field in voids is particularly insensitive to baryonic physics, so if void density profiles and minima could be measured observationally, they would offer a valuable probe of the nature of dark matter. Furthermore, filaments and walls become cleaner, as the substructures in between have been smoothed out; this leads to a clear, mid-range peak in the density PDF.
We study the relationship between dark-matter haloes and matter in the MIP $N$-body simulation ensemble, which allows precision measurements of this relationship, even deeply into voids. What enables this is a lack of discreteness, stochasticity, and
exclusion, achieved by averaging over hundreds of possible sets of initial small-scale modes, while holding fixed large-scale modes that give the cosmic web. We find (i) that dark-matter-halo formation is greatly suppressed in voids; there is an exponential downturn at low densities in the otherwise power-law matter-to-halo density bias function. Thus, the rarity of haloes in voids is akin to the rarity of the largest clusters, and their abundance is quite sensitive to cosmological parameters. The exponential downturn appears both in an excursion-set model, and in a model in which fluctuations evolve in voids as in an open universe with an effective $Omega_m$ proportional to a large-scale density. We also find that (ii) haloes typically populate the average halo-density field in a super-Poisson way, i.e. with a variance exceeding the mean; and (iii) the rank-order-Gaussianized halo and dark-matter fields are impressively similar in Fourier space. We compare both their power spectra and cross-correlation, supporting the conclusion that one is roughly a strictly-increasing mapping of the other. The MIP ensemble especially reveals how halo abundance varies with `environmental quantities beyond the local matter density; (iv) we find a visual suggestion that at fixed matter density, filaments are more populated by haloes than clusters.
We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field, motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic relation is an e
xtension of the linear relation, motivated by the continuity equation, in which the density field is assumed to be proportional to the divergence of the displacement field; we compare the linear and logarithmic relations by measuring both of these fields directly in a cosmological N-body simulation. The relative success of the logarithmic and linear relations depends on the scale at which the density field is smoothed. Thus we explore several ways of measuring the density field, including Cloud-In-Cell smoothing, adaptive smoothing, and the (scale-independent) Delaunay tessellation, and we use both a Fourier space and a geometrical tessellation approach to measuring the divergence. We find that the relation between the divergence of the displacement field and the density is significantly tighter with a logarithmic density variable, especially at low redshifts and for very small (~2 Mpc/h) smoothing scales. We find that the grid-based methods are more reliable than the tessellation-based method of calculating both the density and the divergence fields, though in both cases the logarithmic relation works better in the appropriate regime, which corresponds to nonlinear scales for the grid-based methods and low densities for the tessellation-based method.
We present the SpineWeb framework for the topological analysis of the Cosmic Web and the identification of its walls, filaments and cluster nodes. Based on the watershed segmentation of the cosmic density field, the SpineWeb method invokes the local
adjacency properties of the boundaries between the watershed basins to trace the critical points in the density field and the separatrices defined by them. The separatrices are classified into walls and the spine, the network of filaments and nodes in the matter distribution. Testing the method with a heuristic Voronoi model yields outstanding results. Following the discussion of the test results, we apply the SpineWeb method to a set of cosmological N-body simulations. The latter illustrates the potential for studying the structure and dynamics of the Cosmic Web.
We analyze the structure and connectivity of the distinct morphologies that define the Cosmic Web. With the help of our Multiscale Morphology Filter (MMF), we dissect the matter distribution of a cosmological $Lambda$CDM N-body computer simulation in
to cluster, filaments and walls. The MMF is ideally suited to adress both the anisotropic morphological character of filaments and sheets, as well as the multiscale nature of the hierarchically evolved cosmic matter distribution. The results of our study may be summarized as follows: i).- While all morphologies occupy a roughly well defined range in density, this alone is not sufficient to differentiate between them given their overlap. Environment defined only in terms of density fails to incorporate the intrinsic dynamics of each morphology. This plays an important role in both linear and non linear interactions between haloes. ii).- Most of the mass in the Universe is concentrated in filaments, narrowly followed by clusters. In terms of volume, clusters only represent a minute fraction, and filaments not more than 9%. Walls are relatively inconspicous in terms of mass and volume. iii).- On average, massive clusters are connected to more filaments than low mass clusters. Clusters with $M sim 10^{14}$ M$_{odot}$ h$^{-1}$ have on average two connecting filaments, while clusters with $M geq 10^{15}$ M$_{odot}$ h$^{-1}$ have on average five connecting filaments. iv).- Density profiles indicate that the typical width of filaments is 2$Mpch$. Walls have less well defined boundaries with widths between 5-8 Mpc h$^{-1}$. In their interior, filaments have a power-law density profile with slope ${gamma}approx -1$, corresponding to an isothermal density profile.
