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We study the statistical properties of the eigenvalues of the primordial tidal and deformation tensor for two-dimensional random Gaussian cosmic density fields. With the tidal and deformation tensors, Hessians of the gravitational and velocity potential, being Gaussian, the eigenvalue fields are distinctly non-Gaussian. We extend the Doroshkevich formula for the joined distribution of eigenvalues to two-dimensional fields and evaluate the two- and three-point correlation functions. In addition, we assess the number densities of singular points of the eigenvalue fields and find their corresponding two- and three-point correlation functions. The incentive for the present study is based on our interest in developing a fully analytical theory for the structure and dynamics of the cosmic web. The tidal forces and the resulting mass element deformation shape the prominent anisotropic wall-like and filamentary components of the cosmic web. Less well-known is that the web-like spatial pattern is already recognizable in the primordial tidal and deformation eigenvalue field. Against the full phase-space assessment of structure formation in the Universe, the caustic skeleton theory entails an analytical framework for the non-linear evolution of the cosmic web. It accomplishes this by describing the folding of the dark matter sheet and quantifying the emerging caustic singularities, which are fully specified by the spatial properties of the deformation eigenvalues and eigenvectors. Finally, the eigenvalues of the primordial tidal tensor are crucial in the generation of the angular momentum of galaxies. Understanding their spatial distribution is a critical element in predicting the resulting rotation amplitude and orientation. [ABSTRACT FROM AUTHOR]

Using a set of Lambda cold dark matter simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study, we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers. [ABSTRACT FROM AUTHOR]

We explore the evolution of halo spins in the cosmic web using a very large sample of dark matter haloes in the Lambda cold dark matter Planck-Millennium N -body simulation. We use the nexus+ multiscale formalism to identify the hierarchy of filaments and sheets of the cosmic web at several redshifts. We find that at all times the magnitude of halo spins correlates with the web environment, being largest in filaments, and, for the first time, we show that it also correlates with filament thickness as well as the angle between spin orientation and the spine of the host filament. For example, massive haloes in thick filaments spin faster than their counterparts in thin filaments, while for low-mass haloes the reverse is true. We have also studied the evolution of alignment between halo spin orientations and the preferential axes of filaments and sheets. The alignment varies with halo mass, with the spins of low-mass haloes being predominantly along the filament spine, while those of high-mass haloes being predominantly perpendicular to the filament spine. On average, for all halo masses, halo spins become more perpendicular to the filament spine at later times. At all redshifts, the spin alignment shows a considerable variation with filament thickness, with the halo mass corresponding to the transition from parallel to perpendicular alignment varying by more than one order of magnitude. The cosmic web environmental dependence of halo spin magnitude shows little evolution for z ≤ 2 and is likely a consequence of the correlations in the initial conditions or high redshift effects. [ABSTRACT FROM AUTHOR]

We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after a cosmic evolution observed in redshift space. Previous works on density reconstruction did not self-consistently consider redshift space distortions or included an additional iterative distortion correction step. We present here the analytic solution of coherent flows within a Hamiltonian Monte Carlo posterior sampling of the primordial density field. We test our method within the Zel'dovich approximation, presenting also an analytic solution including tidal fields and spherical collapse on small scales. Our resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true field defined by our mock observations. Novel algorithmic implementations are introduced regarding the mass assignment kernels when defining the dark matter density field and optimization of the time-step in the Hamiltonian equations of motions. Our algorithm, dubbed barcode , promises to be specially suited for analysis of the dark matter cosmic web down to scales of a few megaparsecs. This large-scale structure is implied by the observed spatial distribution of galaxy clusters – such as obtained from X-ray, Sunyaev–Zel'dovich, or weak lensing surveys – as well as that of the intergalactic medium sampled by the Ly α forest or perhaps even by deep hydrogen intensity mapping. In these cases, virialized motions are negligible, and the tracers cannot be modelled as point-like objects. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm. [ABSTRACT FROM AUTHOR]

We investigate the alignment of haloes with the filaments of the cosmic web using an unprecedently large sample of dark matter haloes taken from the P-Millennium Lambda cold dark matter cosmological N -body simulation. We use the state-of-the-art nexus morphological formalism which, due to its multiscale nature, simultaneously identifies structures at all scales. We find strong and highly significant alignments, with both the major axis of haloes and their peculiar velocity tending to orient along the filament. However, the spin–filament alignment displays a more complex trend changing from preferentially parallel at low masses to preferentially perpendicular at high masses. This 'spin flip' occurs at an average mass of |$5\times 10^{11}\, h^{-1}\, \mathrm{M}_\odot$|⁠. This mass increases with increasing filament diameter, varying by more than an order of magnitude between the thinnest and thickest filament samples. We also find that the inner parts of haloes have a spin flip mass that is several times smaller than that of the halo as a whole. These results confirm that recent accretion is responsible for the complex behaviour of the halo spin–filament alignment. Low-mass haloes mainly accrete mass along directions perpendicular to their host filament and thus their spins tend to be oriented along the filaments. In contrast, high-mass haloes mainly accrete along their host filaments and have their spins preferentially perpendicular to them. Furthermore, haloes located in thinner filaments are more likely to accrete along their host filaments than haloes of the same mass located in thicker filaments. [ABSTRACT FROM AUTHOR]

The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low-density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web - depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper, we bring 12 of these methods together and apply them to the same data set in order to understand how they compare. In general, these cosmic-web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore, one would not a priori expect agreement between different techniques; however, many of these methods do converge on the identification of specific features. In this paper, we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find a substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. Mhalo ~ 1013.5 h-1M☉) as being in filaments. Lastly, so that any future cosmic-web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public. [ABSTRACT FROM AUTHOR]

The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our understanding of the formation and evolution of galaxies. The density range of clusters, walls and voids are relatively well separated, when compared to filaments, which span a relatively larger range. The large scale filamentary network thus forms an intricate part of the cosmic web. In this paper, we describe Felix, a topology based framework for visual exploration of filaments in the cosmic web. The filamentary structure is represented by the ascending manifold geometry of the 2-saddles in the Morse-Smale complex of the density field. We generate a hierarchy of Morse-Smale complexes and query for filaments based on the density ranges at the end points of the filaments. The query is processed efficiently over the entire hierarchical Morse-Smale complex, allowing for interactive visualization. We apply Felix to computer simulations based on the heuristic Voronoi kinematic model and the standard $\Lambda$ CDM cosmology, and demonstrate its usefulness through two case studies. First, we extract cosmic filaments within and across cluster like regions in Voronoi kinematic simulation datasets. We demonstrate that we produce similar results to existing structure finders. Second, we extract different classes of filaments based on their density characteristics from the $\Lambda$ CDM simulation datasets. Filaments that form the spine of the cosmic web, which exist in high density regions in the current epoch, are isolated using Felix. Also, filaments present in void-like regions are isolated and visualized. These filamentary structures are often over shadowed by higher density range filaments and are not easily characterizable and extractable using other filament extraction methodologies. [ABSTRACT FROM PUBLISHER]

We use the distribution of maximum circular velocities, Vmax, of satellites in the Milky Way (MW) to constrain the virial mass, M200, of the Galactic halo under an assumed prior of a Λ cold dark matter universe. This is done by analysing the subhalo populations of a large sample of haloes found in the Millennium II cosmological simulation. The observation that the MW has at most three subhaloes with Vmax ≥ 30 km s-1 requires a halo mass M200 ≤ 1.4 × 1012 M⊙, while the existence of the Magellanic Clouds (assumed to have Vmax ≥ 60 km s-1) requires M200 ≥ 1.0 × 1012 M⊙. The first of these conditions is necessary to avoid the 'too-big-to-fail' problem highlighted by Boylan-Kolchin et al., while the second stems from the observation that massive satellites like the Magellanic Clouds are rare. When combining both requirements, we find that the MW halo mass must lie in the range 0.25 ≤ M200/(1012 M⊙) ≤ 1.4 at 90 per cent confidence. The gap in the abundance of Galactic satellites between 30 km s-1 ≤ Vmax ≤ 60 km s-1 places our galaxy in the tail of the expected satellite distribution. [ABSTRACT FROM AUTHOR]

We study the substructure population of Milky Way (MW)-mass haloes in the Λ cold dark matter (ΛCDM) cosmology using a novel procedure to extrapolate subhalo number statistics beyond the resolution limit of N-body simulations. The technique recovers the mean and the variance of the subhalo abundance, but not its spatial distribution. It extends the dynamic range over which precise statistical predictions can be made by the equivalent of performing a simulation with 50 times higher resolution, at no additional computational cost. We apply this technique to MW-mass haloes, but it can easily be applied to haloes of any mass. We find up to 20 per cent more substructures in MW-mass haloes than found in previous studies. Our analysis lowers the mass of the MW halo required to accommodate the observation that the MW has only three satellites with a maximum circular velocity Vmax ≥ 30 km s-1 in the ΛCDM cosmology. The probability of having a subhalo population similar to that in the MW is 20 per cent for a virial mass, M200 = 1 × 1012 M⊙ and practically zero for haloes more massive than M200 = 2 × 1012 M⊙. [ABSTRACT FROM AUTHOR]

We study the formation and evolution of the cosmic web, using the high-resolution CosmoGrid ΛCDM simulation. In particular, we investigate the evolution of the large-scale structure around void halo groups, and compare this to observations of the VGS-31 galaxy group, which consists of three interacting galaxies inside a large void.The structure around such haloes shows a great deal of tenuous structure, with most of such systems being embedded in intra-void filaments and walls. We use the Nexus+} algorithm to detect walls and filaments in CosmoGrid, and find them to be present and detectable at every scale. The void regions embed tenuous walls, which in turn embed tenuous filaments. We hypothesize that the void galaxy group of VGS-31 formed in such an environment. [ABSTRACT FROM PUBLISHER]

We investigate the characteristics and the time evolution of the cosmic web from redshift, z=2, to present time, within the framework of the \nexus{} algorithm. This necessitates the introduction of new analysis tools optimally suited to describe the very intricate and hierarchical pattern that is the cosmic web. In particular, we characterising filaments (walls) in terms of their linear (surface) mass density, which is very good in capturing the evolution of these structures. At early times the cosmos is dominated by tenuous filaments and sheets, which, during subsequent evolution, merge together, such that the present day web is dominated by fewer, but much more massive, structures. We show also that voids are more naturally described in terms of their boundaries and not their centres. We illustrate this for void density profiles, which, when expressed as a function of the distance from void boundary, show a universal profile in good qualitative agreement with the theoretical shell-crossing framework of expanding underdense regions. [ABSTRACT FROM PUBLISHER]

We introduce the NEXUS algorithm for the identification of cosmic web environments: clusters, filaments, walls and voids. This is a multiscale and automatic morphological analysis tool that identifies all the cosmic structures in a scale free way, without preference for a certain size or shape. We develop the NEXUS method to incorporate the density, tidal field, velocity divergence and velocity shear as tracers of the cosmic web. We also present the NEXUS+ procedure which, taking advantage of a novel filtering of the density in logarithmic space, is very successful at identifying the filament and wall environments in a robust and natural way.To assess the algorithms we apply them to an N-body simulation. We find that all methods correctly identify the most prominent filaments and walls, while there are differences in the detection of the more tenuous structures. In general, the structures traced by the density and tidal fields are clumpier and more rugged than those present in the velocity divergence and velocity shear fields. We find that the NEXUS+ method captures much better the filamentary and wall networks and is successful in detecting even the fainter structures. We also confirm the efficiency of our methods by examining the dark matter particle and halo distributions. [ABSTRACT FROM AUTHOR]

ABSTRACT We assess the sensitivity of void shapes to the nature of dark energy that was pointed out in recent studies and also investigate whether or not void shapes are useable as an observational probe in galaxy redshift surveys. Our focus is on the evolution of the mean void ellipticity and its underlying physical cause. To this end, we analyse the morphological properties of voids in five sets of cosmological N-body simulations, each with a different nature of dark energy. To address the question of whether galaxy redshift surveys yield sufficiently accurate void morphologies, voids in the dark matter distribution are compared to those in the halo population. Voids are identified using the parameter-free Watershed Void Finder. The effect of redshift distortions is investigated as well. The main conclusions of this study are as follows: (i) the statistically significant sensitivity of voids in the dark matter distribution is confirmed; (ii) the level of clustering as measured by σ8( z) is identified as the main cause of differences in the mean void shape 〈ε〉; and (iii) in the halo and/or galaxy distribution, it is practically unfeasible to distinguish at a statistically significant level between the various cosmologies due to the sparsity and spatial bias of the sample. [ABSTRACT FROM AUTHOR]

We analyse 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 λ cold dark matter N-body computer simulation into cluster, filaments and walls. The MMF is ideally suited to address both the anisotropic morphological character of filaments and sheets, and 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 per cent. Walls are relatively inconspicuous in terms of mass and volume. (iii) On average, massive clusters are connected to more filaments than low-mass clusters. Clusters with have on average two connecting filaments, while clusters with have on average five connecting filaments. (iv) Density profiles indicate that the typical width of filaments is 2. Walls have less well-defined boundaries with widths between 5 and 8 Mpc h. In their interior, filaments have a power-law density profile with slope , corresponding to an isothermal density profile. [ABSTRACT FROM AUTHOR]

We explore the effects of dark matter and dark energy on the dynamical scaling properties of galaxy clusters. We investigate the cluster Faber–Jackson (FJ), Kormendy and Fundamental Plane (FP) relations between the mass, radius and velocity dispersion of cluster-sized haloes in cosmological N-body simulations. The simulations span a wide range of cosmological parameters, representing open, flat and closed Universes. Independently of the cosmology, we find that the simulated clusters are close to a perfect virial state and do indeed define an FP. The fitted parameters of the FJ, Kormendy and FP relationships do not show any significant dependence on Ωm and/or . One outstanding effect is the influence of Ωm on the thickness of the FP. Following the time evolution of our models, we find slight changes of FJ and Kormendy parameters in high-Ωm universe, along with a slight decrease of FP fitting parameters. We also see an initial increase of the FP thickness followed by a convergence to a nearly constant value. The epoch of convergence is later for higher values of Ωm, while the thickness remains constant in the low- models. We also find a continuous increase of the FP thickness in the standard cold dark matter cosmology. There is no evidence that these differences are due to the different power spectrum slopes at cluster scales. From the point of view of the FP, there is little difference between clusters that quietly accreted their mass and those that underwent massive mergers. The principal effect of strong mergers is to significantly change the ratio of the half-mass radius rhalf to the harmonic mean radius rh. [ABSTRACT FROM AUTHOR]

The evolution of marginally bound supercluster-like objects in an accelerating Λ cold dark matter (ΛCDM) Universe is followed, by means of cosmological simulations, from the present time to an expansion factor . The objects are identified on the basis of the binding density criterion introduced by Dünner et al. Superclusters are identified with the ones whose mass , the most massive one with , comparable to the Shapley supercluster. The spatial distribution of the superclusters remains essentially the same after the present epoch, reflecting the halting growth of the cosmic web as Λ gets to dominate the expansion of the Universe. The same trend can be seen in the stagnation of the development of the mass function of virialized haloes and bound objects. The situation is considerably different when looking at the internal evolution, quantified in terms of their shape, compactness and density profile, and substructure in terms of their multiplicity function. We find a continuing evolution from a wide range of triaxial shapes at to almost perfect spherical shapes at . We also find a systematic trend towards a higher concentration. Meanwhile, we see their substructure gradually disappearing, as the surrounding subclumps fall in and merge to form one coherent, virialized system. [ABSTRACT FROM AUTHOR]

Despite a history that dates back at least a quarter of a century, studies of voids in the large-scale structure of the Universe are bedevilled by a major problem: there exist a large number of quite different void-finding algorithms, a fact that has so far got in the way of groups comparing their results without worrying about whether such a comparison in fact makes sense. Because of the recent increased interest in voids, both in very large galaxy surveys and in detailed simulations of cosmic structure formation, this situation is very unfortunate. We here present the first systematic comparison study of 13 different void finders constructed using particles, haloes, and semi-analytical model galaxies extracted from a subvolume of the Millennium simulation. This study includes many groups that have studied voids over the past decade. We show their results and discuss their differences and agreements. As it turns out, the basic results of the various methods agree very well with each other in that they all locate a major void near the centre of our volume. Voids have very underdense centres, reaching below 10 per cent of the mean cosmic density. In addition, those void finders that allow for void galaxies show that those galaxies follow similar trends. For example, the overdensity of void galaxies brighter than is found to be smaller than about −0.8 by all our void finding algorithms. [ABSTRACT FROM AUTHOR]

We investigate the shapes and mutual alignment of voids in the large-scale matter distribution of a Λ cold dark matter (ΛCDM) cosmology simulation. The voids are identified using the novel watershed void finder (WVF) technique. The identified voids are quite non-spherical and slightly prolate, with axis ratios in the order of . Their orientations are strongly correlated with significant alignments spanning scales . We also find an intimate link between the cosmic tidal field and the void orientations. Over a very wide range of scales we find a coherent and strong alignment of the voids with the tidal field computed from the smoothed density distribution. This orientation–tide alignment remains significant on scales exceeding twice the typical void size, which shows that the long-range external field is responsible for the alignment of the voids. This confirms the view that the large-scale tidal force field is the main agent for the large-scale spatial organization of the cosmic web. [ABSTRACT FROM AUTHOR]

We present a model for the distribution of void sizes and its evolution in the context of hierarchical scenarios of gravitational structure formation. We find that at any cosmic epoch the voids have a size distribution that is well-peaked about a characteristic void size that evolves self-similarly in time. This is in distinct contrast to the distribution of virialized halo masses, which does not have a small-scale cut-off. In our model, the fate of voids is ruled by two processes. The first process affects those voids which are embedded in larger underdense regions: the evolution is effectively one in which a larger void is made up by the mergers of smaller voids, and is analogous to how massive clusters form from the mergers of less massive progenitors. The second process is unique to voids, and occurs to voids that happen to be embedded within a larger-scale overdensity: these voids get squeezed out of existence as the overdensity collapses around them. It is this second process which produces the cut-off at small scales. In the excursion set formulation of cluster abundance and evolution, the solution of the cloud-in-cloud problem, i.e. counting as clusters only those objects which are not embedded in larger clusters, requires the study of random walks crossing one barrier. We show that a similar formulation of void evolution requires the study of a two-barrier problem: one barrier is required to account for voids-in-voids, and the other for voids-in-clouds. Thus, in our model, the void size distribution is a function of two parameters, one of which reflects the dynamics of void formation, and the other the formation of collapsed objects. [ABSTRACT FROM AUTHOR]