The Clustering of Lyman-break Galaxies

We calculate the statistical clustering of Lyman-break galaxies predicted in a selection of currently-fashionable structure formation scenarios. These models are all based on the cold dark matter model, but vary in the amount of dark matter, the initial perturbation spectrum, the background cosmology and in the presence or absence of a cosmological constant term. If Lyman-break galaxies form as a result of hierarchical merging, the amplitude of clustering depends quite sensitively on the minimum halo mass that can host such a galaxy. Interpretation of the recent observations by Giavalisco et al. (1998) would therefore be considerably clarified by a direct determination of the relevant halo properties. For a typical halo mass around $10^{11} h^{-1} M_\odot$ the observations do not discriminate strongly between cosmological models, but if the appropriate mass is larger, say $10^{12} ~h^{-1} M_\odot$ (which seems likely on theoretical grounds), then the data strongly favour models with a low matter-density.Comment: 6 pages, Latex using MN style, 2 figures enclosed. Version accepted for publication in MNRA

Contribution to the Three--Point Function of the Cosmic Microwave Background from the Rees--Sciama Effect

We compute the contribution to the three--point temperature correlation function of the Cosmic Microwave Background coming from the non--linear evolution of Gaussian initial perturbations, as described by the Rees--Sciama (or integrated Sachs--Wolfe) effect. By expressing the collapsed three--point function in terms of multipole amplitudes, we are able to calculate its expectation value for any power spectrum and for any experimental setting on large angular scales. We also give an analytical expression for the {\it rms} collapsed three--point function arising from the cosmic variance of a Gaussian fluctuation field. In the case of {\it COBE} DMR, we find that the predicted signal is about three orders of magnitude below that expected from the cosmic variance.Comment: uuencoded compressed postscript, 10 pages text, 2 pages figure

The galaxy velocity field and CDM models

It is generally accepted that some kind of non-baryonic dark matter accounts for most of the mass density of the universe. Considering such a component has become, in the last decade, a key ingredient in current theories of structure formation. In particular, the Cold Dark Matter (CDM) scenario has proven to be quite successful in explaining most of the observed properties of galaxies and of their large-scale distribution. The standard CDM model is characterized by a primordial Zel'dovich spectrum, of random-phase adiabatic perturbations in a universe with density parameter omega sub 0 = 1 and vanishing cosmological constant. This poster paper presents an analysis of observational data on peculiar motion of optical galaxies in comparison to the predictions of CDM models where the assumptions of the standard scenario: omega sub 0 = 1, n = 1, and bias parameter b = 1 are relaxed. In particular, CDM models with 0 less than n less than 1 and 0.4 less than omega sub 0 less than 1 are considered

The correlation function of X-ray galaxy clusters in the RASS1 Bright Sample

We analyse the spatial clustering properties of the RASS1 Bright Sample, an X-ray flux-limited catalogue of galaxy clusters selected from the southern part of the $ROSAT$ All-Sky Survey. The two-point correlation function $\xi(r)$ of the whole sample is well fitted (in an Einstein-de Sitter model) by the power-law $\xi=(r/r_0)^{-\gamma}$, with $r_0= 21.5^{+3.4}_{-4.4} h^{-1}$ Mpc and $\gamma=2.11^{+0.53}_{-0.56}$ (95.4 per cent confidence level with one fitting parameter). We use the RASS1 Bright Sample as a first application of a theoretical model which aims at predicting the clustering properties of X-ray clusters in flux-limited surveys for different cosmological scenarios. The model uses the theoretical and empirical relations between mass, temperature and X-ray cluster luminosity, and fully accounts for the redshift evolution of the underlying dark matter clustering and cluster bias factor. The comparison between observational results and theoretical predictions shows that the Einstein-de Sitter models display too low a correlation length, while models with a matter density parameter $\Omega_{\rm 0m}=0.3$ (with or without a cosmological constant) are successful in reproducing the observed clustering. The dependence of the correlation length $r_0$ on the X-ray limiting flux and luminosity of the sample is generally consistent with the predictions of all our models. Quantitative agreement is however only reached for $\Omega_{\rm 0m} = 0.3$ models. The model presented here can be reliably applied to future deeper X-ray cluster surveys: the study of their clustering properties will provide a useful complementary tool to the traditional cluster abundance analyses to constrain the cosmological parameters.Comment: 11 pages, Latex using MN style, 4 figures enclosed. Version accepted for publication in MNRA

The epoch of structure formation in blue mixed dark matter models

Recent data on the high--redshift abundance of damped Ly$\alpha$ systems are compared with theoretical predictions for `blue' (i.e. $n>1$) Mixed Dark Matter models. The results show that decreasing the hot component fraction $\Omega_\nu$ and/or increasing the primordial spectral index $n$ implies an earlier epoch of cosmic structure formation. However, we also show that varying $\Omega_\nu$ and $n$ in these directions makes the models barely consistent with the observed abundance of galaxy clusters. Therefore, requiring at the same time observational constraints on damped Ly$\alpha$ systems and cluster abundance to be satisfied represents a challenge for the Mixed Dark Matter class of models.Comment: Uuencoded compressed tar file containing 6 page TeX file and 4 postscript figures. Uses mn.sty and psfig.sty. To appear in MNRAS. Main change: inclusion of a discussion of the constraints coming from the cluster abundance

Eulerian Perturbation Theory in Non-Flat Universes: Second-Order Approximation

The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.Comment: 17 pages, Latex (mn.sty), 1 figure, revised version (1 figure is dropped; eq.46 is corrected and some consequent results are re-discussed), to be published in Monthly Notices of the Royal Astronomical Societ

Excursion set approach to the clustering of dark matter haloes in Lagrangian space

We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the `excursion set' approach by Bond et al., which automatically accounts for the `cloud-in-cloud' problem in the identification of bound systems. Our method allows to calculate correlation functions of haloes in Lagrangian space using either a multi-dimensional Fokker-Planck equation with suitable boundary conditions or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical predictions for the halo auto-correlation function considered in the literature and find good agreement with the results recently obtained within a treatment of halo clustering in terms of `counting fields' by Catelan et al.. The possible effect of spatial correlations on numerical simulations of halo merger trees is finally discussed.Comment: LaTeX, 19 pages, 3 figures. Submitted to MNRA

Testing the Frozen-Flow Approximation

We investigate the accuracy of the frozen--flow approximation (FFA), recently proposed by Matarrese \etal (1992), for following the nonlinear evolution of cosmological density fluctuations under gravitational instability. We compare a number of statistics between results of the FFA and nbody simulations, including those used by Melott, Pellman \& Shandarin (1993) to test the Zel'dovich approximation. The FFA performs reasonably well in a statistical sense, e.g. in reproducing the counts--in--cell distribution, at small scales, but it does poorly in the crosscorrelation with nbody which means it is generally not moving mass to the right place, especially in models with high small--scale power.Comment: 13 pages in TEX (plus 8 Figures but only figs 5,6,7,8 are available--and here enclosed as postscript files, due to size problems), DAPD-93-25

Constraints on primordial non-Gaussianity from WMAP7 and Luminous Red Galaxies power spectrum and forecast for future surveys

We place new constraints on the primordial local non-Gaussianity parameter f_NL using recent Cosmic Microwave Background anisotropy and galaxy clustering data. We model the galaxy power spectrum according to the halo model, accounting for a scale dependent bias correction proportional to f_NL/k^2. We first constrain f_NL in a full 13 parameters analysis that includes 5 parameters of the halo model and 7 cosmological parameters. Using the WMAP7 CMB data and the SDSS DR4 galaxy power spectrum, we find f_NL=171\pm+140 at 68% C.L. and -69<f_NL<+492 at 95% C.L.. We discuss the degeneracies between f_NL and other cosmological parameters. Including SN-Ia data and priors on H_0 from Hubble Space Telescope observations we find a stronger bound: -35<f_NL<+479 at 95% C.L.. We also fit the more recent SDSS DR7 halo power spectrum data finding, for a \Lambda-CDM+f_NL model, f_NL=-93\pm128 at 68% C.L. and -327<f_{NL}<+177 at 95% C.L.. We finally forecast the constraints on f_NL from future surveys as EUCLID and from CMB missions as Planck showing that their combined analysis could detect f_NL\sim 5.Comment: 10 pages, 5 figures, 3 table