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.
Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological simulation
, delineating the structures according to their outer folds. Structure identification is a crucial step in comparing cosmological simulations to observed maps of the Universe. The ORIGAMI definition is objective, dynamical and geometric: filament, wall and void particles are classified according to the number of orthogonal axes along which dark-matter streams have crossed. Here, we briefly review these ideas, and speculate on how ORIGAMI might be useful to find cosmic voids.
We measure the average temperature decrement on the cosmic microwave background (CMB) produced by voids selected in the SDSS DR7 spectroscopic redshift galaxy catalog, spanning redshifts $0<z<0.44$. We find an imprint of amplitude between 2.6 and 2.9
$mu K$ as viewed through a compensated top-hat filter scaled to the radius of each void; we assess the statistical significance of the imprint at ~2$sigma$. We make crucial use of $N$-body simulations to calibrate our analysis. As expected, we find that large voids produce cold spots on the CMB through the Integrated Sachs-Wolfe (ISW) effect. However, we also find that small voids in the halo density field produce hot spots, because they reside in contracting, larger-scale overdense regions. This is an important effect to consider when stacking CMB imprints from voids of different radius. We have found that the same filter radius that gives the largest ISW signal in simulations also yields close to the largest detected signal in the observations. However, although it is low in significance, our measured signal is much higher-amplitude than expected from ISW in the concordance $Lambda$CDM universe. The discrepancy is also at the ~2$sigma$ level. We have demonstrated that our result is robust against the varying of thresholds over a wide range.
We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIG
AMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along 3 orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids respectively. We compare this method to a standard Friends-of-Friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms.
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 construct a map of the time derivative of the gravitational potential traced by SDSS Luminous Red Galaxies. The potential decays on large scales due to cosmic acceleration, leaving an imprint on cosmic microwave background (CMB) radiation through
the integrated Sachs-Wolfe (ISW) effect. With a template fit, we directly measure this signature on the CMB at a 2-sigma confidence level. The measurement is consistent with the cross-correlation statistic, strengthening the claim that dark energy is indeed the cause of the correlation. This new approach potentially simplifies the cosmological interpretation. Our constructed linear ISW map shows no evidence for degree-scale cold and hot spots associated with supervoid and supercluster structures. This suggests that the linear ISW effect in a concordance Lambda-CDM cosmology is insufficient to explain the strong CMB imprints from these structures that we previously reported.
We measure hot and cold spots on the microwave background associated with supercluster and supervoid structures identified in the Sloan Digital Sky Survey Luminous Red Galaxy catalog. The structures give a compelling visual imprint, with a mean tempe
rature deviation of 9.6 +/- 2.2 microK, i.e. above 4 sigma. We interpret this as a detection of the late-time Integrated Sachs-Wolfe (ISW) effect, in which cosmic acceleration from dark energy causes gravitational potentials to decay, heating or cooling photons passing through density crests or troughs. In a flat universe, the linear ISW effect is a direct signal of dark energy.
