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The Calar Alto Void Integral-field Treasury surveY (CAVITY) is a legacy project aimed at characterising the population of galaxies inhabiting voids, which are the most under-dense regions of the cosmic web, located in the Local Universe. This paper describes the first public data release (DR1) of CAVITY, comprising science-grade optical data cubes for the initial 100 out of a total of $\sim$300 galaxies in the Local Universe ($0.005 < z < 0.050$). These data were acquired using the integral-field spectrograph PMAS/PPak mounted on the 3.5m telescope at the Calar Alto observatory. The DR1 galaxy sample encompasses diverse characteristics in the color-magnitude space, morphological type, stellar mass, and gas ionisation conditions, providing a rich resource for addressing key questions in galaxy evolution through spatially resolved spectroscopy. The galaxies in this study were observed with the low-resolution V500 set-up, spanning the wavelength range 3745-7500 \AA, with a spectral resolution of 6.0 \AA\ (FWHM). Here, we describe the data reduction and characteristics and data structure of the CAVITY datasets essential for their scientific utilisation, highlighting such concerns as vignetting effects, as well as the identification of bad pixels and management of spatially correlated noise. We also provide instructions for accessing the CAVITY datasets and associated ancillary data through the project's dedicated database., Comment: 17 pages, 9 figures, 5 tables. Accepted for publication in A&A (replacement after minor language edits)

The observation that accelerated cosmic expansion is dominant since the Mega-parsec cosmic structure became nonlinear seems like an extraordinary coincidence, unless the acceleration is somehow driven by the emergence of the structure. That has given rise to the controversial concept of a gravitational backreaction through which inhomogeneity becomes a driver of accelerated expansion. The standard route when studying strongly inhomogeneous cosmological models is to take either a perturbative approach or a spatial averaging approach. Here we argue that because backreaction is in fact a nonlinear multiscale phenomenon, perturbative approaches may have a limited validity. The alternative is the proposed averaging approach. In this paper we demonstrate that the implied backreaction terms are artificial, that is gauge dependent, which may easily cause ambiguous estimates of its significance. In the current study, we forward a formal fully geometric framework of cosmic foliations in the context of relativistic cosmology. Here we show that fixing a foliation of spacetime determines a choice of gauge. Addressing the correspondence between the metric tensor and the foliation allows us to clarify the theoretical implications of choosing a foliation. Within the context of backreaction, this formalism allows us to discuss the complications of averaging. It reveals that spatial averaging can induce artificial backreaction terms that arise from any specific choice of gauge. Averaging methods presented so far all encounter this problem. Within our foliation framework, we can produce a gauge invariant method of averaging by considering a group of proper time foliations which any cosmic observe can agree upon. We demonstrate that this implies the gauge invariance of the averaging procedure. This makes it applicable to standard cosmological simulations., Comment: arXiv admin note: text overlap with arXiv:2310.19451

On the largest scales the universe appears to be almost perfectly homogeneous and isotropic, adhering to the cosmological principle. On smaller scales inhomogeneities and anisotropies become increasingly prominent, reflecting the origin, emergence and formation of structure in the Universe and its cosmological impact. Also, a range of tensions between various cosmological observations may suggest it to be necessary to explore the consequences of such deviations from the ideal uniform universe. In this study, we restrict this to an investigation of anisotropies on the nature of the Universe. This motivates a more thorough understanding of the manifestation of anisotropy in cosmological applications. When letting go of the assumption of isotropy, spacetime metrics become homogeneous and completely anisotropic. As such, the Lie algebras of Killing vector fields will be 3D, and fit into the so-called 9-part Bianchi classification. This work strives to, given a suitable 3D Lie algebra of vector fields $\{\xi_a\}_{a=1,2,3}$ reconstruct the basis for a metric on which this Lie algebra is Killing. Through finding a determining equation for the frame invariant under $\{\xi_a\}$ and using the method of characteristics to solve it, expressions for said invariant frame in terms of the $\{\xi_a\}$ are obtained. This leads to general equations for the invariant frame in terms of the $\{\xi_a\}$, organized by Bianchi class. Some examples demonstrating this method are worked out., Comment: V2: added Theorem detailing use in arbitrary hom. metrics, and gave further context on links with mathematics

This study concerns an inventory of the gravitational force and tidal field induced by filaments, walls, cluster nodes and voids on Megaparsec scales and how they assemble and shape the Cosmic Web. The study is based on a N$_{\rm Part}=512^3$ $\Lambda$CDM dark matter only N-body simulation in a (300$h^{-1}$~Mpc)$^3$ box at $z=0$. We invoke the density field NEXUS+ multiscale morphological procedure to assign the appropriate morphological feature to each location. We then determine the contribution by each of the cosmic web components to the local gravitational and tidal forces. We find that filaments are, by far, the dominant dynamical component in the interior of filaments, in the majority of underdense void regions and in all wall regions. The gravitational influence of cluster nodes is limited, and they are only dominant in their immediate vicinity. The force field induced by voids is marked by divergent outflowing patterns, yielding the impression of a segmented volume in which voids push matter towards their boundaries. Voids manifest themselves strongly in the tidal field as a cellular tapestry that is closely linked to the multiscale cosmic web. However, even within the interior of voids, the dynamical influence of the surrounding filaments is stronger than the outward push by voids. Therefore, the dynamics of voids cannot be understood without taking into account the influence of the environment. We conclude that filaments constitute the overpowering gravitational agent of the cosmic web, while voids are responsible for the cosmic web's spatial organisation and hence of its spatial connectivity., Comment: 33 pages, 21 figures (Including the appendix). Submitted to MNRAS

Our objectives are to map the filamentary network around the Fornax-Eridanus Complex and probe the influence of the local environment on galaxy morphology. We employ the novel machine-learning tool, 1-DREAM (1-Dimensional, Recovery, Extraction, and Analysis of Manifolds) to detect and model filaments around the Fornax cluster. We then use the morphology-density relation of galaxies to examine the variation in the galaxies' morphology with respect to their distance from the central axis of the detected filaments. We detect 27 filaments that vary in length and galaxy-number density around the Fornax-Eridanus Complex. These filaments showcase a variety of environments; some filaments encompass groups/clusters, while others are only inhabited by galaxies in pristine filamentary environments. We also reveal a well-known structure -- the Fornax Wall, that passes through the Dorado group, Fornax cluster, and Eridanus supergroup. Regarding the morphology of galaxies, we find that early-type galaxies (ETGs) populate high-density filaments and high-density regions of the Fornax Wall. Furthermore, the fraction of ETGs decreases as the distance to the filament spine increases. Of the total galaxy population in filaments, ~7% are ETGs and ~24% are late-type galaxies (LTGs) located in pristine environments of filaments, while ~27% are ETGs and ~42% are LTGs in groups/clusters within filaments. This study reveals the Cosmic Web around the Fornax Cluster and asserts that filamentary environments are heterogeneous in nature. When investigating the role of the environment on galaxy morphology, it is essential to consider both, the local number-density and a galaxy's proximity to the filament spine. Within this framework, we ascribe the observed morphological segregation in the Fornax Wall to pre-processing of galaxies within groups embedded in it., Comment: Accepted for publication in A&A. 21 pages with 15 figures

Cosmic filaments are the main transport channels of matter in the Megaparsec universe, and represent the most prominent structural feature in the matter and galaxy distribution. Here we describe and define the physical and dynamical nature of cosmic filaments. It is based on the realization that the complex spatial pattern and connectivity of the cosmic web are already visible in the primordial random Gaussian density field, in the spatial pattern of the primordial tidal and deformation eigenvalue field. The filaments and other structural features in the cosmic web emerging from this are multistream features and structural singularities in phase-space. The caustic skeleton formalism allows a fully analytical classification, identification, and treatment of the nonlinear cosmic web. The caustic conditions yield the mathematical specification of weblike structures in terms of the primordial deformation tensor eigenvalue and eigenvector fields, in which filaments are identified -- in 2D -- with the so-called cusp caustics. These are centered around points that are maximally stretched as a result of the tidal force field. The resulting mathematical conditions represent a complete characterization of filaments in terms of their formation history, dynamics, and orientation. We illustrate the workings of the formalism on the basis of a set of constrained $N$-body simulations of protofilament realizations. These realizations are analyzed in terms of spatial structure, density profiles, and multistream structure and compared to simpler density or potential field saddle point specifications. The presented formalism, and its 3D generalization, will facilitate the mining of the rich cosmological information contained in the observed weblike galaxy distribution, and be of key significance for the analysis of cosmological surveys such as SDSS, DESI, and Euclid.

The Universe is shaped as a web-like structure, formed by clusters, filaments, and walls that leave large volumes in between named voids. Galaxies in voids have been found to be of a later type, bluer, less massive, and to have a slower evolution than galaxies in denser environments (filaments and walls). However, the effect of the void environment on their stellar population properties is still unclear. We aim to address this question using 118 optical integral field unit datacubes from the Calar Alto Void Integral-field Treasury surveY (CAVITY), observed with the PMAS/PPaK spectrograph at the 3.5m telescope at the Calar Alto Observatory (Almer\'ia, Spain). We used the non-parametric full spectral fitting code STARLIGHT to estimate their stellar population properties: stellar mass, stellar mass surface density, age, star formation rate (SFR), and specific star formation rate (sSFR). We analysed the results through the global and spatially resolved properties. Then, we compared them with a control sample of galaxies in filaments and walls from the CALIFA survey, matched in stellar mass and morphological type. Key findings include void galaxies having a slightly higher half-light radius (HLR), lower stellar mass surface density, and younger ages across all morphological types, and slightly elevated SFR and sSFR (only significant enough for Sas). Many of these differences appear in the outer parts of spiral galaxies in voids (HLR > 1), which are younger and exhibit a higher sSFR, indicative of less evolved discs. This trend is also found for early-type spirals, suggesting a slower transition from star-forming to quiescent states in voids. Our analysis indicates that void galaxies, influenced by their surroundings, undergo a more gradual evolution, especially in their outer regions, with a more pronounced effect for low-mass galaxies., Comment: 24 pages, 22 figures, 5 tables. Accepted for publication in A&A. Updated references list

The large-scale environment of the cosmic web is believed to impact galaxy evolution, but there is still no consensus regarding the mechanisms. We use a semi-analytic model (SAM) galaxy catalog to study the star formation and dust content of local galaxies in different cosmic environments of the cosmic web, namely voids, filaments, walls, and nodes. We find a strong impact of the environment only for galaxies with $M_{\rm stars}\lesssim10^{10.8}\, M_\odot$: the less dense the environment, the larger the star formation rate and dust content at fixed stellar mass. This is attributed to the fact that galaxies in less dense environments typically feature younger stellar populations, a slower evolution of their stellar mass and a delayed star formation compared to galaxies in denser environments. As for galaxies with $M_{\rm stars}\gtrsim 10^{10.8}\, M_\odot$ differences among environments are milder due to the disc instability (DI) driven supermassive black hole (SMBH) growth implemented in the SAM, which makes SMBH growth, and thus galaxy quenching, environment insensitive. We qualitatively test our predictions against observations by identifying environments in the SDSS-DR16 using dust masses derived from the GAMA survey. The agreement is encouraging, particularly at ${\rm log} \, M_{\rm stars}/M_\odot\gtrsim 10.5-11$, where sSFRs and dust masses appear quite environment-insensitive. This result confirms the importance of in situ growth channels of SMBHs., Comment: 21 pages, 12 figures, 3 tables. Accepted for publication in ApJ

The observation that accelerated cosmic expansion appears to start around the time that nonlinear cosmic structure is appearing seems like an extraordinary coincidence, unless the acceleration is somehow driven by the emergence of the structure. That has given rise to the controversial concept of a gravitational backreaction through which inhomogeneity becomes a driver of accelerated expansion. The standard route when studying strongly inhomogeneous cosmological models is to take either a perturbative approach or a spatial averaging approach. Here we argue that because backreaction is in fact a nonlinear multiscale phenomenon, perturbative approaches may have a limited validity. With respect to the currently proposed averaging approaches we here show that they lead to gauge dependent backreaction and hence ambiguous estimates of its magnitude. In the present study, we formalise inhomogeneous cosmic evolution within the framework of foliations of spacetime. Fixing a foliation amounts to making a gauge choice. Addressing the correspondence between the metric tensor and the foliation allows us to clarify the implications of choosing a foliation for the representation of equivalent cosmologies. It is important to note that, within the context of backreaction, this formalism allows us to discuss the vagaries of averaging in the framework of spacetime foliations. It reveals that spatial averaging can induce artificial, i.e. gauge dependent, backreaction terms that arise from any specific choice of gauge. Averaging methods presented so far all encounter this problem. However, within our foliation framework, we can produce a gauge invariant method of averaging by invoking the gauge-invariant Bardeen formalism for cosmological perturbation theory. We demonstrate that this implies the gauge invariance of the averaging procedure. This makes it applicable to standard cosmological simulations., Comment: 21 pages, 3 figures, typos fixed in v2

Void galaxies are essential for understanding the physical processes that drive galaxy evolution because they are less affected by external factors than galaxies in denser environments, that is, in filaments, walls, and clusters. The stellar metallicity of a galaxy traces the accumulated fossil record of the star formation through the entire life of the galaxy. A comparison of the stellar metallicity of galaxies in various environments, including voids, filaments, walls, and clusters can provide valuable insights into how the large-scale environment affects the chemical evolution of the galaxy. We present the first comparison of the relation of the total stellar mass versus central stellar metallicity between galaxies in voids, filaments, walls, and clusters with different star formation history (SFH) types, morphologies, and colours for stellar masses between $10^{8.0}$ to $10^{11.5}$ solar masses and redshift $0.01

We study the statistical properties of the eigenvalues of the primordial tidal and deformation tensor for random Gaussian cosmic density fields. With the tidal and deformation tensors, Hessians of the gravitational and velocity potential, being Gaussian, the corresponding eigenvalue fields are distinctly non-Gaussian. Following the extension of the Doroshkevich formula for the joined distribution of eigenvalues to two-dimensional fields, we evaluate the two- and three-point correlation functions of the eigenvalue fields. 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 role of tidal forces and the resulting mass element deformation in shaping the prominent anisotropic wall-like and filamentary components of the cosmic web has since long been recognized based on the Zel'dovich approximation. Less well-known is that the weblike spatial pattern is already recognizable in the primordial tidal and deformation eigenvalue field, even while the corresponding Gaussian density and the potential field appear merely as a spatially incoherent and unstructured random field. Furthermore, against the background of a full phase-space assessment of structure formation in the Universe, the caustic skeleton theory entails a fully analytical framework for the nonlinear evolution of the cosmic web. It describes the folding of the dark matter sheet and the emerging caustic singularities, fully specified by the deformation eigenvalues and eigenvectors. Finally, tidal tensor eigenvalues are of central importance, and understanding their distribution is critical in predicting the resulting rotation and orientation. The current study applies to two-dimensional Gaussian random fields and will be generalized to a three-dimensional analysis in an upcoming study., Comment: 21 pages, 10 figures

The cosmic web consists of a complex configuration of voids, walls, filaments, and clusters, which formed under the gravitational collapse of Gaussian fluctuations. Understanding under what conditions these different structures emerge from simple initial conditions, and how different cosmological models influence their evolution, is central to the study of the large-scale structure. Here, we present a general formalism for setting up initial random density and velocity fields satisfying non-linear constraints for specialized N-body simulations. These allow us to link the non-linear conditions on the eigenvalue and eigenvector fields of the deformation tensor, as specified by caustic skeleton theory, to the current-day cosmic web. By extending constrained Gaussian random field theory, and the corresponding Hoffman-Ribak algorithm, to non-linear constraints, we probe the statistical properties of the progenitors of the walls, filaments, and clusters of the cosmic web. Applied to cosmological N-body simulations, the proposed techniques pave the way towards a systematic investigation of the evolution of the progenitors of the present-day walls, filaments, and clusters, and the embedded galaxies, putting flesh on the bones of the caustic skeleton. The developed nonlinear constrained random field theory is valid for generic cosmological conditions. For ease of visualization, the case study presented here probes the two-dimensional caustic skeleton., Comment: 68 pages, 18 figures

We study the topology of the network of ionized and neutral regions that characterized the intergalactic medium during the Epoch of Reionization. Our analysis uses the formalism of persistent homology, which offers a highly intuitive and comprehensive description of the ionization topology in terms of the births and deaths of topological features. Features are identified as $k$-dimensional holes in the ionization bubble network, whose abundance is given by the $k$th Betti number: $\beta_0$ for ionized bubbles, $\beta_1$ for tunnels, and $\beta_2$ for neutral islands. Using semi-numerical models of reionization, we investigate the dependence on the properties of sources and sinks of ionizing radiation. Of all topological features, we find that the tunnels dominate during reionization and that their number is easiest to observe and most sensitive to the astrophysical parameters of interest, such as the gas fraction and halo mass necessary for star formation. Seen as a phase transition, the importance of the tunnels can be explained by the entanglement of two percolating clusters and the fact that higher-dimensional features arise when lower-dimensional features link together. We also study the relation between the morphological components of the bubble network (bubbles, tunnels, islands) and those of the cosmic web (clusters, filaments, voids), describing a correspondence between the $k$-dimensional features of both. Finally, we apply the formalism to mock observations of the 21-cm signal. Assuming 1000 observation hours with HERA Phase II, we show that astrophysical models can be differentiated and confirm that persistent homology provides additional information beyond the power spectrum., Comment: 18 pages, 12 figures, MNRAS, accepted with minor revisions

We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalise clustering up to the second-order correlation function, and use our systematic topological analysis to correlate local information and properties of haloes with their multi-scale geometrical environment of the cosmic web (elongated filamentary bridges and sheetlike walls). We capture the multi-scale topology traced by the halo distribution through filtrations of the corresponding Delaunay tessellation. The resulting nested $\textit{alpha shapes}$ are sensitive to the local density, perfectly outline the local geometry, and contain the complete information on the multi-scale topology. We find a remarkable linear relationship between halo masses and topology: haloes of different mass trace environments with different topological signature. This is $\textit{topological bias}$, an environmental structure bias independent of the halo clustering bias associated with the two-point correlation function. This mass-dependent linear scaling relation allows us to take clustering into account and determine the overall connectivity from a limited sample of galaxies. The presence of topological bias has major implications for the study of voids and filaments in the observed distribution of galaxies. The (infra)structure and shape of these key cosmic web components will strongly depend on the underlying galaxy sample. Their use as cosmological probes, with their properties influenced by cosmological parameters, will have to account for the subtleties of topological bias. This is of particular relevance with the large upcoming galaxy surveys such as DESI, Euclid, and the Vera Rubin telescope surveys., Comment: Revised manuscript after review. 29 pages, 11 figures

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

The alignment between halo spins and the cosmic web is still poorly understood despite being a widely studied topic. Here, we study this alignment within the context of tidal torque theory (TTT) and deviations from it. To this end, we analyze the evolution of the shape and spin direction of proto-haloes, i.e. of all the volume elements associated to a $z=0$ halo, with respect to the present-day filaments. We find that the major axis of proto-haloes undergoes a major change, from being strongly perpendicular to the filament spine in the initial conditions, to being preferentially aligned at the present time. In comparison, the spin orientation shows only a mild evolution: it starts slightly parallel to the filament spine, but the subsequent evolution, up to $z{\sim}1$, gradually changes its orientation to preferentially perpendicular. In order to analyze these signals in the TTT framework, we split the haloes according to their net spin growth with respect to the median TTT expectation, finding a clear correlation with the spin--filament alignment. At the present time, haloes whose spin grew the most are the ones most perpendicular to the filament spine, while haloes whose spin grew below the median TTT expectation are typically more aligned. The dependence of spin directions on net spin growth is already present in the initial conditions, and gets further modified by late-time, $z<2$, evolution. Also, spin directions mildly deviate from the TTT predictions even at high redshift, indicating the need for extensions to the model., Comment: 19 pages, 12 figures, accepted in MNRAS

Using a set of $\Lambda$CDM 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., Comment: 23 pages, 14 figures, 1 table. Revised and shortened version, submitted to MNRAS

Using a set of high-resolution simulations we study the statistical correlation of dark matter halo properties with the large-scale environment. We consider halo populations split into four Cosmic Web (CW) elements: voids, walls, filaments, and nodes. For the first time we present a study of CW effects for halos covering six decades in mass: $10^{8}-10^{14}{h^{-1}{\rm M}_{\odot}}$. We find that the fraction of halos living in various web components is a strong function of mass, with the majority of $M>10^{12}{h^{-1}{\rm M}_{\odot}}$ halos living in filaments and nodes. Low mass halos are more equitably distributed in filaments, walls, and voids. For halo density profiles and formation times we find a universal mass threshold of $M_{th}\sim6\times10^{10}{h^{-1}{\rm M}_{\odot}}$ below which these properties vary with environment. Here, filament halos have the steepest concentration-mass relation, walls are close to the overall mean, and void halos have the flattest relation. This amounts to $c_{200}$ for filament and void halos that are respectively $14\%$ higher and $7\%$ lower than the mean at $M=2\times10^8{h^{-1}{\rm M}_{\odot}}$, with low-mass node halos being most likely splashed-back. We find double power-law fits that very well describe $c(M)$ for the four environments in the whole probed mass range. A complementary picture is found for the average formation times, with the mass-formation time relations following trends shown for the concentrations: the nodes halos being the oldest and void halo the youngest. The CW environmental effect is much weaker when studying the halo spin and shapes. The trends with halo mass is reversed: the small halos with $M<10^{10}{h^{-1}{\rm M}_{\odot}}$ seem to be unaffected by the CW environment. Some weak trends are visible for more massive void and walls halos, which, on average, are characterized by lower spin and higher triaxiality parameters., Comment: 18 pages, 9 figures, match the published version in Physical Review D eid. 063517

We explore the evolution of halo spins in the cosmic web using a very large sample of dark matter haloes in the $\Lambda$CDM 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 also have 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 environmental dependence of halo spin magnitude shows little evolution for $z\leq2$ and is likely a consequence of the correlations in the initial conditions or high redshift effects, Comment: Accepted for publication in MNRAS. Main results in figures 7, 9 and 12

The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial non-Gaussianities would form a valuable clue on the physics of the early Universe. The virtue of both the Euler characteristic and the Minkowski functionals in general, lies in the fact that there exist closed form expressions for their expectation values for Gaussian random fields. However, the Euler characteristic and Minkowski functionals are summarizing characteristics of topology and geometry. Considerably more topological information is contained in the homology of the random field, as it completely describes the creation, merging and disappearance of topological features in superlevel set filtrations. In the present study we extend the topological analysis of the superlevel set filtrations of two-dimensional Gaussian random fields by analysing the statistical properties of the Betti numbers - counting the number of connected components and loops - and the persistence diagrams - describing the creation and mergers of homological features. Using the link between homology and the critical points of a function - as illustrated by the Morse-Smale complex - we derive a one-parameter fitting formula for the expectation value of the Betti numbers and forward this formalism to the persistent diagrams. We, moreover, numerically demonstrate the sensitivity of the Betti numbers and persistence diagrams to the presence of non-Gaussianities.

We investigate the alignment of galaxies and haloes relative to cosmic web filaments using the EAGLE hydrodynamical simulation. We identify filaments by applying the NEXUS+ method to the mass distribution and the Bisous formalism to the galaxy distribution. Both web finders return similar filamentary structures that are well aligned and that contain comparable galaxy populations. EAGLE haloes have an identical spin alignment with filaments as their counterparts in dark matter only simulations: a complex mass dependent trend with low mass haloes spinning preferentially parallel to and high mass haloes spinning preferentially perpendicular to filaments. In contrast, galaxy spins do not show such a spin transition and have a propensity for perpendicular alignments at all masses, with the degree of alignment being largest for massive galaxies. This result is valid for both NEXUS+ and Bisous filaments. When splitting by morphology, we find that elliptical galaxies show a stronger orthogonal spin--filament alignment than spiral galaxies of similar mass. The same is true of their haloes, with the host haloes of elliptical galaxies having a larger degree of orthogonal alignment than the host haloes of spirals. Due to the misalignment between galaxy shape and spin, galaxy minor axes are oriented differently with filaments than galaxy spins. We find that the galaxies whose minor axis is perpendicular to a filament are much better aligned with their host haloes. This suggests that many of the same physical processes determine both the galaxy--filament and the galaxy--halo alignments., Comment: 18 pages, 13 figures. Submitted to MNRAS

Cosmic voids, the less dense patches of the Universe, are promising laboratories to extract cosmological information. Thanks to their unique low density character, voids are extremely sensitive to diffuse components such as neutrinos and dark energy, and represent ideal environments to study modifications of gravity, where the effects of such modifications are expected to be more prominent. Robust void-related observables, including for example redshift-space distortions (RSD) and weak lensing around voids, are a promising way to chase and test new physics. Cosmological analysis of the large-scale structure of the Universe predominantly relies on the high density regions. Current and upcoming surveys are designed to optimize the extraction of cosmological information from these zones, but leave voids under-exploited. A dense, large area spectroscopic survey with imaging capabilities is ideal to exploit the power of voids fully. Besides helping illuminate the nature of dark energy, modified gravity, and neutrinos, this survey will give access to a detailed map of under-dense regions, providing an unprecedented opportunity to observe and study a so far under-explored galaxy population., Comment: Science White Paper for the Astro2020 Decadal Survey, 5 pages text, 14 pages with references and affiliations

We study the topology generated by the temperature fluctuations of the Cosmic Microwave Background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the LCDM paradigm with Gaussian distributed fluctuations. The survey of the CMB over $\mathbb{S}^2$ is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of "masks" is of importance, we introduce the concept of relative homology. The parametric $\chi^2$-test shows differences between observations and simulations, yielding $p$-values at per-cent to less than per-mil levels roughly between 2 to 7 degrees. The highest observed deviation for $b_0$ and $b_1$ is approximately between $3\sigma$-4$\sigma$ at scales of 3 to 7 degrees. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66 degrees in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck's predecessor WMAP satellite. The mildly anomalous behaviour of Euler characteristic is related to the strongly anomalous behaviour of components and holes. These are also the scales at which the observed maps exhibit low variance compared to the simulations. Non-parametric tests show even stronger differences at almost all scales. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate to look at primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology., Comment: 18 pages, 16 figures, 3 tables, submitted to Astronomy \& Astrophysics

This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers $\beta_0$, $\beta_1$ and $\beta_2$. We show that Betti numbers entail a considerably richer characterization of the topology of the primordial density field. Of particular interest is that Betti numbers specify which topological features - islands, cavities or tunnels - define its spatial structure. A principal characteristic of Gaussian fields is that the three Betti numbers dominate the topology at different density ranges. At extreme density levels, the topology is dominated by a single class of features. At low levels this is a \emph{Swiss-cheeselike} topology, dominated by isolated cavities, at high levels a predominantly \emph{Meatball-like} topology of isolated objects. At moderate density levels, two Betti number define a more \emph{Sponge-like} topology. At mean density, the topology even needs three Betti numbers, quantifying a field consisting of several disconnected complexes, not of one connected and percolating overdensity. A {\it second} important aspect of Betti number statistics is that they are sensitive to the power spectrum. It reveals a monotonic trend in which at a moderate density range a lower spectral index corresponds to a considerably higher (relative) population of cavities and islands. We also assess the level of complementary information that Betti numbers represent, in addition to conventional measures such as Minkowski functionals. To this end, we include an extensive description of the Gaussian Kinematic Formula (GKF), which represents a major theoretical underpinning for this discussion., Comment: 44 pages, 27 Figures, 2 Tables, accepted for publication in MNRAS in the original version. This version updates references and fixes typos

We present a new formalism for studying the topology of HII regions during the Epoch of Reionisation, based on persistent homology theory. With persistent homology, it is possible to follow the evolution of topological features over time. We introduce the notion of a persistence field as a statistical summary of persistence data and we show how these fields can be used to identify different stages of reionisation. We identify two new stages common to all bubble ionisation scenarios. Following an initial pre-overlap and subsequent overlap stage, the topology is first dominated by neutral filaments (filament stage) and then by enclosed patches of neutral hydrogen undergoing outside-in ionisation (patch stage). We study how these stages are affected by the degree of galaxy clustering. We also show how persistence fields can be used to study other properties of the ionisation topology, such as the bubble size distribution and the fractal-like topology of the largest ionised region., Comment: 18 pages, 12 figures, 1 table. Submitted to MNRAS

We present a self-consistent Bayesian formalism to sample the primordial density fields compatible with a set of dark matter density tracers after 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 using augmented Lagrangian perturbation theory. Our resulting reconstructed fields are isotropic and their power spectra are unbiased compared to the true one 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, SZ or weak lensing surveys --- as well as that of the intergalactic medium sampled by the Lyman alpha forest or perhaps even by deep hydrogen intensity mapping. In these cases, virialized motions are negligible, and the tracers cannot be modeled as point-like objects. It could be used in all of these contexts as a baryon acoustic oscillation reconstruction algorithm., Comment: 34 pages, 25 figures, 1 table. Submitted to MNRAS. Accompanying code at https://github.com/egpbos/barcode

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 $\Lambda$CDM 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 $5\times10^{11}~h^{-1}M_\odot$. 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., Comment: Accepted to MNRAS on 16th August 2018

For over twenty years, the term 'cosmic web' has guided our understanding of the large-scale arrangement of matter in the cosmos, accurately evoking the concept of a network of galaxies linked by filaments. But the physical correspondence between the cosmic web and structural-engineering or textile 'spiderwebs' is even deeper than previously known, and extends to origami tessellations as well. Here we explain that in a good structure-formation approximation known as the adhesion model, threads of the cosmic web form a spiderweb, i.e. can be strung up to be entirely in tension. The correspondence is exact if nodes sampling voids are included, and if structure is excluded within collapsed regions (walls, filaments and haloes), where dark-matter multistreaming and baryonic physics affect the structure. We also suggest how concepts arising from this link might be used to test cosmological models: for example, to test for large-scale anisotropy and rotational flows in the cosmos., Comment: Accepted to Royal Society Open Science. See illustrative adhesion-model Python notebook: https://github.com/jhidding/adhesion-example/tree/master/notebook and interactive spiderweb-design Python notebook: https://github.com/neyrinck/sectional-tess, runnable without installation at https://mybinder.org/v2/gh/neyrinck/sectional-tess/master

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 twelve 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 {\it 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 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. $M_{\rm halo}\sim10^{13.5}h^{-1}M_{\odot}$) 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., Comment: 24 pages, 8 figures, 2 tables. Submitted to MN. Comments Welcome

We present a general formalism for identifying the caustic structure of an evolving mass distribution in an arbitrary dimensional space. For the class of Hamiltonian fluids the identification corresponds to the classification of singularities in Lagrangian catastrophe theory. Based on this we develop a theoretical framework for the formation of the cosmic web, and specifically those aspects that characterize its unique nature: its complex topological connectivity and multiscale spinal structure of sheetlike membranes, elongated filaments and compact cluster nodes. The present work represents an extension of the work by Arnol'd et al., who classified the caustics for the 1- and 2-dimensional Zel'dovich approximation. His seminal work established the role of emerging singularities in the formation of nonlinear structures in the universe. At the transition from the linear to nonlinear structure evolution, the first complex features emerge at locations where different fluid elements cross to establish multistream regions. The classification and characterization of these mass element foldings can be encapsulated in caustic conditions on the eigenvalue and eigenvector fields of the deformation tensor field. We introduce an alternative and transparent proof for Lagrangian catastrophe theory, and derive the caustic conditions for general Lagrangian fluids, with arbitrary dynamics, including dissipative terms and vorticity. The new proof allows us to describe the full 3-dimensional complexity of the gravitationally evolving cosmic matter field. One of our key findings is the significance of the eigenvector field of the deformation field for outlining the spatial structure of the caustic skeleton. We consider the caustic conditions for the 3-dimensional Zel'dovich approximation, extending earlier work on those for 1- and 2-dimensional fluids towards the full spatial richness of the cosmic web.

We forecast the scientific capabilities to improve our understanding of cosmic inflation of CORE, a proposed CMB space satellite submitted in response to the ESA fifth call for a medium-size mission opportunity. The CORE satellite will map the CMB anisotropies in temperature and polarization in 19 frequency channels spanning the range 60-600 GHz. CORE will have an aggregate noise sensitivity of $1.7 \mu$K$\cdot \,$arcmin and an angular resolution of 5' at 200 GHz. We explore the impact of telescope size and noise sensitivity on the inflation science return by making forecasts for several instrumental configurations. This study assumes that the lower and higher frequency channels suffice to remove foreground contaminations and complements other related studies of component separation and systematic effects, which will be reported in other papers of the series "Exploring Cosmic Origins with CORE." We forecast the capability to determine key inflationary parameters, to lower the detection limit for the tensor-to-scalar ratio down to the $10^{-3}$ level, to chart the landscape of single field slow-roll inflationary models, to constrain the epoch of reheating, thus connecting inflation to the standard radiation-matter dominated Big Bang era, to reconstruct the primordial power spectrum, to constrain the contribution from isocurvature perturbations to the $10^{-3}$ level, to improve constraints on the cosmic string tension to a level below the presumptive GUT scale, and to improve the current measurements of primordial non-Gaussianities down to the $f_{NL}^{\rm local} < 1$ level. For all the models explored, CORE alone will improve significantly on the present constraints on the physics of inflation. Its capabilities will be further enhanced by combining with complementary future cosmological observations., Comment: Latex 107 pages, revised with updated author list and minor modifications

We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESA's fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the impact of various instrumental options, in particular the telescope size and sensitivity level, and review the great, transformative potential of the mission as proposed. Specifically, we assess the impact on a broad range of fundamental parameters of our Universe as a function of the expected CMB characteristics, with other papers in the series focusing on controlling astrophysical and instrumental residual systematics. In this paper, we assume that only a few central CORE frequency channels are usable for our purpose, all others being devoted to the cleaning of astrophysical contaminants. On the theoretical side, we assume LCDM as our general framework and quantify the improvement provided by CORE over the current constraints from the Planck 2015 release. We also study the joint sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale Structure experiments like DESI and Euclid. Specific constraints on the physics of inflation are presented in another paper of the series. In addition to the six parameters of the base LCDM, which describe the matter content of a spatially flat universe with adiabatic and scalar primordial fluctuations from inflation, we derive the precision achievable on parameters like those describing curvature, neutrino physics, extra light relics, primordial helium abundance, dark matter annihilation, recombination physics, variation of fundamental constants, dark energy, modified gravity, reionization and cosmic birefringence. (ABRIDGED), Comment: 90 pages, 25 Figures. Revised version with new authors list and references

Voids form a prominent aspect of the Megaparsec distribution of galaxies and matter. Not only do they represent a key constituent of the Cosmic Web, they also are one of the cleanest probes and measures of global cosmological parameters. The shape and evolution of voids are highly sensitive to the nature of dark energy, while their substructure and galaxy population provides a direct key to the nature of dark matter. Also, the pristine environment of void interiors is an important testing ground for our understanding of environmental influences on galaxy formation and evolution. In this paper, we review the key aspects of the structure and dynamics of voids, with a particular focus on the hierarchical evolution of the void population. We demonstrate how the rich structural pattern of the Cosmic Web is related to the complex evolution and buildup of voids., Comment: 28 pages, 13 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia; added arxiv reference to journal citation.

The Zeldovich approximation (ZA) predicts the formation of a web of singularities. While these singularities may only exist in the most formal interpretation of the ZA, they provide a powerful tool for the analysis of initial conditions. We present a novel method to find the skeleton of the resulting cosmic web based on singularities in the primordial deformation tensor and its higher order derivatives. We show that the A_3-lines predict the formation of filaments in a two-dimensional model. We continue with applications of the adhesion model to visualise structures in the local (z < 0.03) universe., Comment: 9 pages, 8 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

We describe the Bayesian BARCODE formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the basis of observational data, without the need for a correction of redshift space artifacts. In this contribution we provide a general overview of the the Cosmic Web connection with clusters and a description of the Bayesian BARCODE formalism. We conclude with a presentation of its successful workings with respect to test runs based on a simulated large scale matter distribution, in physical space as well as in redshift space., Comment: 18 pages, 8 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

In 1970 Zel'dovich published a far-reaching paper presenting a simple equation describing the nonlinear growth of primordial density inhomogeneities. The equation was remarkably successful in explaining the large scale structure in the Universe that we observe: a Universe in which the structure appears to be delineated by filaments and clusters of galaxies surrounding huge void regions. In order to concretise this impression it is necessary to define these structural elements through formal techniques with which we can compare the Zel'dovich model and N-body simulations with the observational data. We present an overview of recent efforts to identify voids, filaments and clusters in both the observed galaxy distribution and in numerical simulations of structure formation. We focus, in particular, on methods that involve no fine-tuning of parameters and that handle scale dependence automatically. It is important that these techniques should result in finding structures that relate directly to the dynamical mechanism of structure formation., Comment: 13 pages, 9 figures. Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia; added reference to section 6

We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure, and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different weblike morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of weblike configurations, and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys., Comment: 31 pages, 24 figures, Published in MNRAS in original version. This version updates the reference list

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. 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., Comment: 14 pages, 9 figures, 2 tables. Accepted for publication in IEEE Transactions on Visualization & Computer Graphics. A detailed description of the project, including the software and the supplementary material is available at http://vgl.serc.iisc.ernet.in/felix/

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 characterize filaments (walls) in terms of their linear (surface) mass density. This 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 also show 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., Comment: 8 pages, 7 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

We present a method, PhotoWeb, for estimating photometric redshifts of individual galaxies, and their equivalent distance, with megaparsec and even sub-megaparsec accuracy using the Cosmic Web as a constraint over photo-z estimates. PhotoWeb redshift errors for individual galaxies are of the order of delta_z = 0.0007, compared to errors of delta_z = 0.02 for current photo-z techniques. The mean redshift error is of the order of 0.00005-0.0004 compared to mean errors in the range delta_z =z 0.001-0.01 for the best available photo-z estimates in the literature. Current photo-z techniques based on the spectral energy distribution of galaxies and projected clustering produce redshift estimates with large errors due to the poor constraining power the galaxy's spectral energy distribution and projected clustering can provide. The Cosmic Web, on the other hand, provides the strongest constraints on the position of galaxies. The network of walls, filaments and voids occupy ~%10 of the volume of the Universe, yet they contain ~%95 of galaxies. The cosmic web, being a cellular system with well-defined boundaries, sets a restricted set of intermittent positions a galaxy can occupy along a given line-of-sight. Using the information in the density field computed from spectroscopic redshifts we can narrow the possible locations of a given galaxy along the line of sight from a single broad probability distribution (from photo-z) to one or a few narrow peaks. Our first results improve previous photo-z errors by more than one order of magnitude allowing sub-megaparsec errors in some cases. Such accurate estimates for tens of millions of galaxies will allow unprecedented galaxy-LSS studies. In this work we apply our technique to the SDSS photo-z galaxy sample and discuss its performance and future improvements., Comment: Final version submitted to MNRAS

The cosmic web is a complex spatial pattern of walls, filaments, cluster nodes and underdense void regions. It emerged through gravitational amplification from the Gaussian primordial density field. Here we infer analytical expressions for the spatial statistics of caustics in the evolving large-scale mass distribution. In our analysis, following the quasi-linear Zeldovich formalism and confined to the 1D and 2D situation, we compute number density and correlation properties of caustics in cosmic density fields that evolve from Gaussian primordial conditions. The analysis can be straightforwardly extended to the 3D situation. We moreover, are currently extending the approach to the non-linear regime of structure formation by including higher order Lagrangian approximations and Lagrangian effective field theory., Comment: 8 pages, 3 figures, Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

We study the formation and evolution of the cosmic web, using the high-resolution CosmoGrid \$\Lambda\$CDM 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., Comment: 5 pages, 3 figures, 1 table; Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

Voids represent a unique environment for the study of galaxy evolution, as the lower density environment is expected to result in shorter merger histories and slower evolution of galaxies. This provides an ideal opportunity to test theories of galaxy formation and evolution. Imaging of the neutral hydrogen, central in both driving and regulating star formation, directly traces the gas reservoir and can reveal interactions and signs of cold gas accretion. For a new Void Galaxy Survey (VGS), we have carefully selected a sample of 59 galaxies that reside in the deepest underdensities of geometrically identified voids within the SDSS at distances of ~100 Mpc, and pursued deep UV, optical, Halpha, IR, and HI imaging to study in detail the morphology and kinematics of both the stellar and gaseous components. This sample allows us to not only examine the global statistical properties of void galaxies, but also to explore the details of the dynamical properties. We present an overview of the VGS, and highlight key results on the HI content and individually interesting systems. In general, we find that the void galaxies are gas rich, low luminosity, blue disk galaxies, with optical and HI properties that are not unusual for their luminosity and morphology. We see evidence of both ongoing assembly, through the gas dynamics between interacting systems, and significant gas accretion, seen in extended gas disks and kinematic misalignments. The VGS establishes a local reference sample to be used in future HI surveys (CHILES, DINGO, LADUMA) that will directly observe the HI evolution of void galaxies over cosmic time., Comment: 7 pages, 5 figures. Proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web", 23-28 June 2014, Tallinn, Estonia

We use the distribution of maximum circular velocities, $V_{max}$, of satellites in the Milky Way (MW) to constrain the virial mass, $M_{200}$, of the Galactic halo under an assumed prior of a $\Lambda$CDM universe. This is done by analysing the subhalo populations of a large sample of halos found in the Millennium II cosmological simulation. The observation that the MW has at most three subhalos with $V_{max}\ge30 km/s$ requires a halo mass $M_{200}\le1.4\times10^{12} M_\odot$, while the existence of the Magellanic Clouds (assumed to have $V_{max}\ge60 km/s$) requires $M_{200}\ge1.0\times10^{12} M_\odot$. 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 $0.25 \le M_{200}/(10^{12} M_\odot) \le 1.4$ at $90\%$ confidence. The gap in the abundance of Galactic satellites between $30 km/s\le V_{max} \le 60 km/s$ places our galaxy in the tail of the expected satellite distribution., Comment: 13 pages, 9 figures, updated to match published version in MNRAS

We study the substructure population of Milky Way (MW)-mass halos in the $\Lambda$CDM 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 halos, but it can easily be applied to halos of any mass. We find up to $20\%$ more substructures in MW-mass halos 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 $V_{max}\ge30 km/s$ in the $\Lambda$CDM cosmology. The probability of having a subhalo population similar to that in the MW is $20\%$ for a virial mass, $M_{200}=1\times10^{12} M_\odot$ and practically zero for halos more massive than $M_{200}=2\times10^{12} M_\odot$., Comment: 17 pages, 14 figures, updated to match published version in MNRAS

The cosmic web is the largest scale manifestation of the anisotropic gravitational collapse of matter. It represents the transitional stage between linear and non-linear structures and contains easily accessible information about the early phases of structure formation processes. Here we investigate the characteristics and the time evolution of morphological components since. Our analysis involves the application of the NEXUS Multiscale Morphology Filter (MMF) technique, predominantly its NEXUS+ version, to high resolution and large volume cosmological simulations. We quantify the cosmic web components in terms of their mass and volume content, their density distribution and halo populations. We employ new analysis techniques to determine the spatial extent of filaments and sheets, like their total length and local width. This analysis identifies cluster and filaments as the most prominent components of the web. In contrast, while voids and sheets take most of the volume, they correspond to underdense environments and are devoid of group-sized and more massive haloes. 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. The analysis of the mass transport between environments clearly shows how matter flows from voids into walls, and then via filaments into cluster regions, which form the nodes of the cosmic web. We also study the properties of individual filamentary branches, to find long, almost straight, filaments extending to distances larger than 100Mpc/h. These constitute the bridges between massive clusters, which seem to form along approximatively straight lines., Comment: 56 pages, 61 figures, accepted for publication in MNRAS

We describe how the dynamics of cosmic structure formation defines the intricate geometric structure of the spine of the cosmic web. The Zeldovich approximation is used to model the backbone of the cosmic web in terms of its singularity structure. The description by Arnold et al. (1982) in terms of catastrophe theory forms the basis of our analysis. This two-dimensional analysis involves a profound assessment of the Lagrangian and Eulerian projections of the gravitationally evolving four-dimensional phase-space manifold. It involves the identification of the complete family of singularity classes, and the corresponding caustics that we see emerging as structure in Eulerian space evolves. In particular, as it is instrumental in outlining the spatial network of the cosmic web, we investigate the nature of spatial connections between these singularities. The major finding of our study is that all singularities are located on a set of lines in Lagrangian space. All dynamical processes related to the caustics are concentrated near these lines. We demonstrate and discuss extensively how all 2D singularities are to be found on these lines. When mapping this spatial pattern of lines to Eulerian space, we find a growing connectedness between initially disjoint lines, resulting in a percolating network. In other words, the lines form the blueprint for the global geometric evolution of the cosmic web., Comment: 37 pages, 21 figures, accepted for publication in MNRAS