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We investigate the evolution of superclusters and supercluster cocoons (basins of attraction), and the influence of cosmological parameters to the evolution. We perform numerical simulations of the evolution of the cosmic web for different cosmological models: the LCDM model with a conventional value of the dark energy (DE) density, the open model OCDM with no DE, the standard SCDM model with no DE, and the Hyper-DE HCDM model with an enhanced DE density value. We find ensembles of superclusters of these models for five evolutionary stages, corresponding to the present epoch z = 0, and to redshifts z = 1, 3, 10, 30. We use diameters of the largest superclusters and the number of superclusters as percolation functions to describe properties of the ensemble of superclusters in the cosmic web. We analyse the size and mass distribution of superclusters in models and in real Sloan Digital Sky Survey (SDSS) based samples. In all models numbers and volumes of supercluster cocoons are independent on cosmological epochs. Supercluster masses increase with time, and geometrical sizes in comoving coordinates decrease with time, for all models. LCDM, OCDM and HCDM models have almost similar percolation parameters. This suggests that the essential parameter, which defines the evolution of superclusters, is the matter density. The DE density influences the growth of the amplitude of density perturbations, and the growth of masses of superclusters, albeit significantly less strongly. The HCDM model has the largest speed of the growth of the amplitude of density fluctuations, and the largest growth of supercluster masses during the evolution. Geometrical diameters and numbers of HCDM superclusters at high threshold densities are larger than for LCDM and OCDM superclusters. SCDM model has about two times more superclusters than other models; SCDM superclusters have smaller diameters and masses., Comment: 14 pages, 10 figures (accepted by Astronomy & Astrophysics). arXiv admin note: text overlap with arXiv:1901.09378

Aims. Our goal is to find the relation between the two-point correlation functions (CFs) of projected and spatial density fields of galaxies in the context of the cosmic web. Methods. To investigate relations between spatial (3D) and projected (2D) CFs of galaxies we used density fields of two simulations: a $\Lambda$-dominated cold dark matter (LCDM) model with known particle data, and the Millennium simulation with know data on simulated galaxies. We compare 3D and 2D correlation functions. In the 2D case, we use samples of various thickness to find the dependence of 2D CFs on the thickness of samples. We also compare 3D CFs in real and redshift space. Results. The dominant elements of the cosmic web are clusters and filaments, separated by voids filling most of the volume. In individual 2D sheets, the positions of clusters and filaments do not coincide. As a result, in projection, the clusters and filaments fill in 2D voids. This leads to a decrease in the amplitudes of CFs (and power spectra) in projection. For this reason, the amplitudes of 2D CFs are lower than the amplitudes of 3D correlation functions: the thicker the 2D sample, the greater the difference. Conclusions. Spatial CFs of galaxies contain valuable information about the geometrical properties of the cosmic web that cannot be found from projected CFs., Comment: 15 pages, 9 figures, 4 tables. Accepted in A&A

We calculated spatial correlation functions of galaxies, $\xi(r)$, structure functions, $g(r)=1 +\xi(r)$, gradient functions, $\gamma(r)= d \log g(r)/ d \log r$, and fractal dimension functions, $D(r)= 3+\gamma(r)$, using dark matter particles of the biased $\Lambda$ cold dark matter (CDM) simulation, observed galaxies of the Sloan Digital Sky Survey (SDSS), and simulated galaxies of the Millennium and EAGLE simulations. We analysed how these functions describe fractal and biasing properties of the cosmic web. The correlation functions of the biased $\Lambda$CDM model samples at small distances (particle and galaxy separations), $r \le 2.25$~\Mpc, describe the distribution of matter inside dark matter (DM) halos. In real and simulated galaxy samples, only the brightest galaxies in clusters are visible, and the transition from clusters to filaments occurs at a distance $r \approx 0.8 - 1.5$~\Mpc. Real and simulated galaxies of low luminosity, $M_r \ge -19$, have almost identical correlation lengths and amplitudes, indicating that dwarf galaxies are satellites of brighter galaxies, and do not form a smooth population in voids. The combination of several physical processes (e.g. the formation of halos along the caustics of particle trajectories and the phase synchronisation of density perturbations on various scales) transforms the initial random density field to the current highly non-random density field. Galaxy formation is suppressed in voids, which increases the amplitudes of correlation functions and power spectra of galaxies, and increases the large-scale bias parameter. The combined evidence leads to the large-scale bias parameter of $L_\star$ galaxies the value $b_\star =1.85 \pm 0.15$. We find $r_0(L_\star) = 7.20 \pm 0.19$ for the correlation length of $L_\star$ galaxies., Comment: 15 pages, 10 figures, 5 tables. The revised version is accepted by Astronomy & Astrophysics

The degeneracy between geometric (Alcock-Paczynski) and dynamic (redshift space) distortions in the pattern of the galaxy distribution has been a long standing problem in the study of the large scale structure of the universe. We examine the possibility of lifting this degeneracy and constraining cosmological parameters by using the Baryon Acoustic Oscillation (BAO) scale as a feature of known physical size, the sound horizon r_s ~ 150 Mpc. We callibrate this scale with the equivalent feature in the Cosmic Microwave Background (CMB). First, we construct a toy model of a power spectrum which includes the BAO as well as geometric and dynamic distortions. By adding a prior onto the sound horizon of ~1% we show, using a Fisher matrix analysis, that error ellipses for line of sight and tangential distortion parameters shrink by a factor of two for a 20(Gpc/h)^3 `DESpec/BigBOSS'-like galaxy survey including shot noise. This improvement is even more marked in smaller surveys. We also carry out a Monte Carlo Nested Sampling analysis on our parameter space. We find that Monte Carlo and Fisher methods can agree reasonably well for surveys with large volume but differ greatly for small volume surveys., Comment: 10 pages, 7 figures, submitted to MNRAS

Our goal is to see how density waves of different scale combine to form voids between galaxy systems of various scale. We perform numerical simulations of structure formation in cubes of size 100 and 256 Mpc/h, with resolutions 256^3 and 512^3 particles and cells. To understand the role of density perturbations of various scale we cut power spectra at scales from 8 to 128 Mpc/h, using in all series identical initial random realisations. We find that small haloes and short filaments form all over the simulation box, if perturbations only up to scale 8 Mpc/h are present. The phenomenon of large multi-scale voids in the cosmic web requires the presence of an extended spectrum of primordial density perturbations. The void phenomenon is due to the action of two processes: the synchronisation of density perturbations of medium and large scales, and the suppression of galaxy formation in low-density regions by the combined action of negative sections of medium- and large-scale density perturbations, so that their densities are less than the mean density, and thus during the evolution their densities decrease., Comment: 16 pages, 11 figures, revised version

We follow the evolution of galaxy systems in numerical simulation. Our goal is to understand the role of density perturbations of various scales in the formation and evolution of the cosmic web. We perform numerical simulations with the full power spectrum of perturbations, and with spectrum cut at long wavelengths. Additionally, we have one model, where we cut the intermediate waves. We analyze the density field and study the void sizes and density field clusters in different models. Our analysis shows that the fine structure (groups and clusters of galaxies) is created by small-scale density perturbations of scale $\leq 8$ \Mpc. Filaments of galaxies and clusters are created by perturbations of intermediate scale from $\sim 8$ to $\sim 32$ \Mpc, superclusters of galaxies by larger perturbations. We conclude that the scale of the pattern of the cosmic web is determined by density perturbations of scale up to $\sim 100$ \Mpc. Larger perturbations do not change the pattern of the web, but modulate the richness of galaxy systems, and make voids emptier. The stop of the increase of the scale of the pattern of the cosmic web with increasing scale of density perturbations can probably be explained as the freezing of the web at redshift $z\simeq 0.7$., Comment: 12 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

According to the modern cosmological paradigm galaxies and galaxy systems form from tiny density perturbations generated during the very early phase of the evolution of the Universe. Using numerical simulations we study the evolution of phases of density perturbations of different scales to understand the formation and evolution of the cosmic web. We apply the wavelet analysis to follow the evolution of high-density regions (clusters and superclusters) of the cosmic web. We show that the positions of maxima and minima of density waves (their spatial phases) almost do not change during the evolution of the structure. Positions of extrema of density perturbations are the more stable, the larger is the wavelength of perturbations. Combining observational and simulation data we conclude that the skeleton of the cosmic web was present already in an early stage of structure evolution., Comment: 12 pages, 8 figures, revised version

We present a morphological study of the two richest superclusters from the 2dF Galaxy Redshift Survey (SCL126, the Sloan Great Wall, and SCL9, the Sculptor supercluster). We use Minkowski functionals, shapefinders, and galaxy group information to study the substructure of these superclusters as formed by different populations of galaxies. We compare the properties of grouped and isolated galaxies in the core region and in the outskirts of superclusters. The fourth Minkowski functional $V_3$ and the morphological signature $K_1$- $K_2$ show a crossover from low-density morphology (outskirts of supercluster) to high-density morphology (core of supercluster) at mass fraction $m_f \approx 0.7$. The galaxy content and the morphology of the galaxy populations in supercluster cores and outskirts is different. The core regions contain a larger fraction of early type, red galaxies, and richer groups than the outskirts of superclusters. In the core and outskirt regions the fine structure of the two prominent superclusters as delineated by galaxies from different populations also differs. Our results suggest that both local (group/cluster) and global (supercluster) environments are important in forming galaxy morphologies and colors (and determining the star formation activity). The differences between the superclusters indicate that these superclusters have different evolutional histories (Abridged)., Comment: 23 pages, accepted for publication in The Astrophysical Journal

We use the 2dF Galaxy Redshift Survey data to compile catalogues of superclusters for the Northern and Southern regions of the 2dFGRS, altogether 543 superclusters at redshifts 0.009 < z < 0.2. We analyse methods of compiling supercluster catalogues and use results of the Millennium Simulation to investigate possible selection effects and errors. We find that the most effective method is the density field method using smoothing with an Epanechnikov kernel of radius 8 Mpc/h. We derive positions of the highest luminosity density peaks and find the most luminous cluster in the vicinity of the peak, this cluster is considered as the main cluster and its brightest galaxy the main galaxy of the supercluster. In catalogues we give equatorial coordinates and distances of superclusters as determined by positions of their main clusters. We also calculate the expected total luminosities of the superclusters., Comment: 16 pages, 11 figures, submitted for Astronomy and Astrophysics. High-resolution pdf file and supplementary data can be found at http://www.aai.ee/~maret/2dfscl.html

In this paper we study the clustering of SZ-selected galaxy clusters on a past light-cone, particularly paying attention to the possibility of constraining properties of dark energy. The prospects of detecting baryonic features in the cluster power spectrum for a wide and shallow survey like PLANCK, and for an SPT-like narrow and deep survey are discussed. It is demonstrated that these future blank sky SZ surveys will have capability to improve significantly over the recently announced detection of baryonic oscillations based on the SDSS Luminous Red Galaxy (LRG) sample. We carry out parameter estimation using Fisher matrix approach taking into account the anisotropic nature of the power spectrum due to redshift space and cosmological distortions. The clustering signal which is not too sensitive to systematic uncertainties serves as a valuable piece of information that in combination with other sources of data helps in breaking degeneracies between the cosmological parameters., Comment: 18 pages, 17 figures, version accepted in A&A

We find clusters and superclusters of galaxies using the Data Release 1 of the Sloan Digital Sky Survey. We determine the luminosity function of clusters and find that clusters in a high-density environment have a luminosity a factor of ~5 higher than in a low-density environment. We also study clusters and superclusters in numerical simulations. Simulated clusters in a high-density environment are also more massive than those in a low-density environment. Comparison of the density distribution at various epochs in simulations shows that in large low-density regions (voids) dynamical evolution is very slow and stops at an early epoch. In contrast, in large regions of higher density (superclusters) dynamical evolution starts early and continues until the present; here particles cluster early, and by merging of smaller groups very rich systems of galaxies form., Comment: 12 pages, 8 figures, submitted for Astronomy and Astrophysics

In this work we consider the changes of the SZ cluster brightness, flux and number counts induced by the motion of the Solar System with respect to the frame defined by the cosmic microwave background (CMB). These changes are connected with the Doppler effect and aberration and exhibit a strong spectral and spatial dependence. The correction to the SZ cluster brightness and flux has an amplitude and spectral dependence, which is similar to the first order cluster peculiar velocity correction to the thermal SZ effect. Due to the change in the received cluster CMB flux the motion of the Solar System induces a dipolar asymmetry in the observed number of clusters above a given flux level. Similar effects were discussed for $\gamma$-ray bursts and radio galaxies, but here, due to the very peculiar frequency-dependence of the thermal SZ effect, the number of observed clusters in one direction of the sky can be both, decreased or increased depending on the frequency band. A detection of this asymmetry should be possible using future full sky CMB experiments with mJy sensitivities., Comment: 7 pages, 6 figures, submitted to Astronomy and Astrophysics, corrected pdf-problem

The luminosity function of galaxies of the Early Data Release of the Sloan Digital Sky Survey (SDSS) and the Las Campanas Redshift Survey (LCRS) is calculated. The luminosity function depends on redshift, density of the environment and is different for the Norther and Southern slice of SDSS. Luminosity functions is used to derive the number and luminosity density fields of galaxies of the SDSS and LCRS surveys with a grid size of 1 h^{-1} Mpc for flat cosmological models with \Omega_m=0.3 and \Omega_\Lambda =0.7. We find that the luminosity function depends on the density of the environment: in high-density regions brightest galaxies are more luminous than in low-density regions by a factor up to 5., Comment: 10 pages LaTeX text, 8 PostScript Figures, 1 jpg Figure (4a, 4b), submitted to Astronomy and Astrophysics