arXiv subjects

S. Matarrese

Publications and source records attributed to S. Matarrese.

At least 145 records · Page 8Linked to original sources

arXiv1998

The nonlinear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e. the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the nonlinear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher-order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N-body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional r.m.s. density fluctuations are $< 0.5$.

astro-ph↗

arXiv1998

Relativistic second-order perturbations of the Einstein-de Sitter Universe

We consider the evolution of relativistic perturbations in the Einstein-de Sitter cosmological model, including second-order effects. The perturbations are considered in two different settings: the widely used synchronous gauge and the Poisson (generalized longitudinal) one. Since, in general, perturbations are gauge dependent, we start by considering gauge transformations at second order. Next, we give the evolution of perturbations in the synchronous gauge, taking into account both scalar and tensor modes in the initial conditions. Using the second-order gauge transformation previously defined, we are then able to transform these perturbations to the Poisson gauge. The most important feature of second-order perturbation theory is mode-mixing, which here also means, for instance, that primordial density perturbations act as a source for gravitational waves, while primordial gravitational waves give rise to second-order density fluctuations. Possible applications of our formalism range from the study of the evolution of perturbations in the mildly non-linear regime to the analysis of secondary anisotropies of the Cosmic Microwave Background.

astro-ph↗

arXiv1998

The bias field of dark matter haloes

This paper presents a stochastic approach to the clustering evolution of dark matter haloes in the Universe. Haloes, identified by a Press-Schechter-type algorithm in Lagrangian space, are described in terms of `counting fields', acting as non-linear operators on the underlying Gaussian density fluctuations. By ensemble averaging these counting fields, the standard Press-Schechter mass function as well as analytic expressions for the halo correlation function and corresponding bias factors of linear theory are obtained, thereby extending the recent results by Mo and White. The non-linear evolution of our halo population is then followed by solving the continuity equation, under the sole hypothesis that haloes move by the action of gravity. This leads to an exact and general formula for the bias field of dark matter haloes, defined as the local ratio between their number density contrast and the mass density fluctuation. Besides being a function of position and `observation' redshift, this random field depends upon the mass and formation epoch of the objects and is both non-linear and non-local. The latter features are expected to leave a detectable imprint on the spatial clustering of galaxies, as described, for instance, by statistics like bispectrum and skewness. Our algorithm may have several interesting applications, among which the possibility of generating mock halo catalogues from low-resolution N-body simulations.

astro-ph↗

arXiv1997

Large-scale bias in the Universe: bispectrum method

Evidence that the Universe may be close to the critical density, required for its expansion eventually to be halted, comes principally from dynamical studies of large-scale structure. These studies either use the observed peculiar velocity field of galaxies directly, or indirectly by quantifying its anisotropic effect on galaxy clustering in redshift surveys. A potential difficulty with both such approaches is that the density parameter $Ω_0$ is obtained only in the combination $β= Ω_0^{0.6}/b$, if linear perturbation theory is used. The determination of the density parameter $Ω_0$ is therefore compromised by the lack of a good measurement of the bias parameter $b$, which relates the clustering of sample galaxies to the clustering of mass. In this paper, we develop an idea of Fry (1994), using second-order perturbation theory to investigate how to measure the bias parameter on large scales. The use of higher-order statistics allows the degeneracy between $b$ and $Ω_0$ to be lifted, and an unambiguous determination of $Ω_0$ then becomes possible. We apply a likelihood approach to the bispectrum, the three-point function in Fourier space. This paper is the first step in turning the idea into a practical proposition for redshift surveys, and is principally concerned with noise properties of the bispectrum, which are non-trivial. The calculation of the required bispectrum covariances involves the six-point function, including many noise terms, for which we have developed a generating functional approach which will be of value in calculating high-order statistics in general.

astro-ph↗

arXiv1996

On Relativistic Perturbations of Second and Higher Order

We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit transformation rules at second order.

gr-qc↗

arXiv1996

Physical constraints on the halo mass function

We analyse the effect of two relevant physical constraints on the mass multiplicity function of dark matter halos in a Press--Schechter type algorithm. Considering the random--walk of linear Gaussian density fluctuations as a function of the smoothing scale, we simultaneously i) account for mass semi--positivity and ii) avoid the cloud--in--cloud problem. It is shown that the former constraint implies a severe cutoff of low--mass objects, balanced by an increase on larger mass scales. The analysis is performed both for scale--free power--spectra and for the standard cold dark matter model. Our approach shows that the well--known ``infrared" divergence of the standard Press--Schechter mass function is caused by unphysical, negative mass events which inevitably occur in a Gaussian distribution of density fluctuations.

astro-ph↗

arXiv1995

Observational constraints on blue primordial spectra

Recently, there has been growing interest on primordial ``blue" ($n>1$) perturbation spectra, motivated both by a composite set of observational data on large scales and from the point of view of theoretical model building. After reviewing the theoretical (inflationary) motivations for these blue spectra, we consider various observational constraints, within both Cold Dark Matter and Mixed Dark Matter scenarios. In particular, using linear theory, we discuss large--scale bulk flows and the X--ray cluster abundance. We also perform various N--body simulations of these models to study the clustering properties of the matter distribution and the peculiar velocity field.

astro-ph↗

arXiv1994

Velocity Fields in Non--Gaussian Cold Dark Matter Models

We analyse the large--scale velocity field obtained by N--body simulations of cold dark matter (CDM) models with non--Gaussian primordial density fluctuations, considering models with both positive and negative primordial skewness in the density fluctuation distribution. We study the velocity probability distribution and calculate the dependence of the bulk flow, one--point velocity dispersion and Cosmic Mach Number on the filtering size. We find that the sign of the primordial skewness of the density field provides poor discriminatory power on the evolved velocity field. All non--Gaussian models here considered tend to have lower velocity dispersion and bulk flow than the standard Gaussian CDM model, while the Cosmic Mach Number turns out to be a poor statistic in characterizing the models. Next, we compare the large--scale velocity field of a composite sample of optically selected galaxies as described by the Local Group properties, bulk flow, velocity correlation function and Cosmic Mach Number, with the velocity field of mock catalogues extracted from the N--body simulations. The comparison does not clearly permit to single out a best model: the standard Gaussian model is however marginally preferred by the maximum likelihood analysis.

astro-ph↗

arXiv1994

A Local View of the Observable Universe

We present results on the non-linear dynamics of inhomogeneous cosmological models with irrotational dust and a positive cosmological constant, considering, in particular, a wide class with vanishing magnetic Weyl tensor. For those patches of the universe that do not recollapse to a singularity we find a unique attractor, representing a de Sitter vacuum phase. For the (re-)collapsing regions we find a family of (Kasner) attractors, so that generically these regions fall in spindle-like singularities. These results give substantial support to the idea that the universe can be very inhomogeneous on ultra-large, super-horizon scales, whit observers living in those (almost) isotropic regions that emerge from an inflationary phase.

astro-ph↗

arXiv1994

Dynamics of Silent Universes

We investigate the local non--linear dynamics of irrotational dust with vanishing magnetic part of the Weyl tensor, $H_{ab}$. Once coded in the initial conditions, this dynamical restriction is respected by the relativistic evolution equations. Thus, the outcome of the latter are {\it exact solutions} for special initial conditions with $H_{ab}=0$, but with no symmetries: they describe inhomogeneous triaxial dynamics generalizing that of a fluid element in a Tolman--Bondi, Kantowski--Sachs or Szekeres geometry. A subset of these solutions may be seen as (special) perturbations of Friedmann models, in the sense that there are trajectories in phase--space that pass arbitrarily close to the isotropic ones. We find that the final fate of ever--expanding configurations is a spherical void, locally corresponding to a Milne universe. For collapsing configurations we find a whole family of triaxial attractors, with vanishing local density parameter $Ω$. These attractors locally correspond to Kasner vacuum solutions: there is a single physical configuration collapsing to a degenerate {\it pancake}, while the generic configuration collapses to a triaxial {\it spindle} singularity. These {\it silent universe} models may provide a fair representation of the universe on super horizon scales. Moreover, one might conjecture that the non--local information carried by $H_{ab}$ becomes negligible during the late highly non--linear stages of collapse, so that the attractors we find may give all of the relevant expansion or collapse configurations of irrotational dust.

astro-ph↗

arXiv1994

A Relativistic Approch to Gravitational Instability in the Expanding Universe: Second Order Lagrangian Solutions

A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and geometric quantities and compared with the corresponding ones in the Newtonian approximation. Specifically, we compute the density, the volume expansion scalar, the shear, the ``electric" part, or tide, and the ``magnetic" part of the Weyl tensor. The evolution of the shear and the tide beyond the linear regime strongly depends on the ratio of the characteristic size of the perturbation to the cosmological horizon distance. For perturbations on sub--horizon scales the usual Newtonian approximation applies, at least at the considered perturbative order; on super--horizon scales, instead, a new picture emerges, which we call ``silent universe", as each fluid element evolves independently of the environment, being unable to exchange signals with the surrounding matter through either sound waves or gravitational radiation. For perturbations inside the Hubble radius particular attention is paid in singling out non--local effects during the non--linear evolution of fluid elements. These non--local effects are shown to be carried by a traceless and divergenceless tensor, contained in the magnetic part of the Weyl tensor, which is dynamically generated as soon as the system evolves away from the linear regime.

astro-ph↗

arXiv1993

The Variance of QSO Counts in Cells

{}From three quasar samples with a total of 1038 objects in the redshift range $1.0 ÷2.2$ we measure the variance $σ^2$ of counts in cells of volume $V_u$. By a maximum likelihood analysis applied separately on these samples we obtain estimates of $σ^2(\ell)$, with $\ell \equiv V_u^{1/3}$. The analysis from a single catalog for $\ell = ~40~h^{-1}$ Mpc and from a suitable average over the three catalogs for $\ell = ~60,~80$ and $100~h^{-1}$ Mpc, gives $σ^2(\ell) = 0.46^{+0.27}_{-0.27}$, $0.18^{+0.14}_{-0.15}$, $0.05^{+0.14}_{-0.05}$ and $0.12^{+0.13}_{-0.12}$, respectively, where the $70\%$ confidence ranges account for both sampling errors and statistical fluctuations in the counts. This allows a comparison of QSO clustering on large scales with analogous data recently obtained both for optical and IRAS galaxies: QSOs seem to be more clustered than these galaxies by a biasing factor $b_{QSO}/b_{gal} \sim 1.4 - 2.3$.

astro-ph↗

arXiv1993

The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models

We analyze the temperature three--point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale anisotropies, such as those measured by the {\em COBE} DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic inflation we are able to provide a {\it universal} expression for the ensemble averaged three--point function and for the corresponding skewness, which accounts for all primordial second--order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a {\em hierarchical} form. Our results are then specialized to a number of relevant models: power--law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non--Gaussian effects are small: as an example, the {\em mean} skewness is much smaller than the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation field.

astro-ph↗

arXiv1993

Weighted Bias and Galaxy Clustering

We consider a weighted biasing scheme for galaxy clustering. This differs from previous treatments in the fact that the biased density field coincides with the background mass--density whenever the latter exceeds a given threshold value. There is some physical motivation for this scheme and it is in better accord with intuitive ideas than models based on the Kaiser (1984) analysis of the clustering of rich clusters. We explain how different classes of object could be biased in different ways with respect to the underlying density distribution but still have $b=1$. We also show that if one applies our scheme consistently a weak dependence of $b$ upon density can be implied. This could also be the reason why the correlation function of galaxies in groups does not differ substantially from the correlation function of all galaxies.

astro-ph↗

arXiv1993

Non--Linear Dynamics of Irrotational Dust: Eulerian and Lagrangian Approaches

Some recently proposed approximations to follow the non--linear evolution of collisionless matter perturbations in the universe are reviewed. The first one, called frozen--flow approximation, is an Eulerian method within Newtonian theory, and is based on neglecting the role of particle inertia compared to the damping implied by the Hubble drag. The second approach is General Relativistic and Lagrangian; it is based on following the evolution of fluid and geometric observables in the rest frame of each fluid element, under the only approximation of neglecting the back--reaction on the system of the gravitational radiation emitted during non--linear collapse.

astro-ph↗

arXiv1993

Blue perturbation spectra from inflation

We investigate inflationary models leading to density perturbations with a spectral index $n>1$ (``blue spectra"). These perturbation spectra may be useful to simultaneously account for both the amount of ultra large-scale power required to fit cosmic microwave background anisotropies, such as those measured by COBE, and that required to give bulk motions and structures on the $\sim 50~h^{-1}$ Mpc scale.

astro-ph↗

arXiv1993

Galaxy Velocity Field in Tilted Cold Dark Matter Models

We study the cosmic peculiar velocity field as traced by a sample of 1184 spiral, elliptical and S0 galaxies, grouped in 704 objects. We carry out a statistical analysis, by calculating bulk flows and velocity correlation functions for this sample and for mock catalogs which we extract from N--body simulations. For the simulations we consider tilted (i.e. with spectral index $n\leq 1$) CDM models with different values of the linear bias parameter $b$. By mean of a maximum likelihood analysis we estimate the ability of the models in fitting the observations as measured by the above statistics and in reproducing the Local Group properties.

astro-ph↗

arXiv1993

Higher Order Moments of the Matter Distribution in Scale--Free Cosmological Simulations with Large Dynamic Range

We calculate reduced moments $\overline ξ_q$ of the matter density fluctuations, up to order $q=5$, from counts in cells produced by Particle--Mesh numerical simulations with scale--free Gaussian initial conditions. We use power--law spectra $P(k) \propto k^n$ with indices $n=-3,~-2,~-1,~0,~1$. Due to the supposed absence of characteristic times or scales in our models, all quantities are expected to depend on a single scaling variable. For each model, the moments at all times can be expressed in terms of the variance $\overline ξ_2$, alone. We look for agreement with the hierarchical scaling ansatz, according to which $\overline ξ_q \propto \overline ξ_2^{~q-1}$. For $n\leq -2$ models we find strong deviations from the hierarchy, which are mostly due to the presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also found in $n \geq -1$ models. For the first time, due to our large dynamic range and careful checks of scaling and shot--noise effects, we are able to detect evolution away from the perturbation theory result.

astro-ph↗