The gravitational wave contribution to CMB anisotropies and the amplitude of mass fluctuations from COBE results

A stochastic background of primordial gravitational waves may substantially contribute, via the Sachs--Wolfe effect, to the large--scale Cosmic Microwave Background (CMB) anisotropies recently detected by COBE. This implies a {\it bias} in any resulting determination of the primordial amplitude of density fluctuations. We consider the constraints imposed on $n<1$ (``tilted") power--law fluctuation spectra, taking into account the contribution from both scalar and tensor waves, as predicted by power--law inflation. The gravitational--wave contribution to CMB anisotropies generally reduces the required {\it rms} level of mass fluctuation, thereby increasing the linear {\it bias parameter}, even in models where the spectral index is close to the Harrison--Zel'dovich value $n=1$. This ``gravitational--wave bias" helps to reconcile the predictions of CDM models with observations on pairwise galaxy velocity dispersion on small scales.Comment: 11 pages. Two figures available upon reques

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.Comment: Revised version (accepted for publication in MNRAS) including a new comparison with numerical results, a new appendix and new references. uuencoded gzip'ed tar archive containing many LaTex files (the main file is mass.tex). 16 pages with 6 figures (all included

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.Comment: 23 pages, LaTeX (included psfig.tex), 4 figures. Few comments and references have been added, and minor typos and errors corrected. This version matches the refereed one, in press in MNRA

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.Comment: 18 pages; LaTeX; 4 PostScript figures included at the end of the file; SISSA REF.193/93/A and DFPD 93/A/8

The Variance of QSO Counts in Cells

{}From three quasar samples with a total of 1038 objects in the redshift range $1.0 \div 2.2$ we measure the variance $\sigma^2$ of counts in cells of volume $V_u$. By a maximum likelihood analysis applied separately on these samples we obtain estimates of $\sigma^2(\ell)$, 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 $\sigma^2(\ell) = 0.46^{+0.27}_{-0.27}$, $0.18^{+0.14}_{-0.15}$, $0.05^{+0.14}_{-0.05}$ 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 $b_{QSO}/b_{gal} \sim 1.4 - 2.3$.Comment: 13 pages in plain Tex, 5 figures available in postscript in a separate file, submitted to ApJ, DAPD-33

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.Comment: 10 pages in Latex with mn.sty (available at the end of the paper

An Isocurvature CDM Cosmogony. I. A Worked Example of Evolution Through Inflation

I present a specific worked example of evolution through inflation to the initial conditions for an isocurvature CDM model for structure formation. The model invokes three scalar fields, one that drives power law inflation, one that survives to become the present-day CDM, and one that gives the CDM field a mass that slowly decreases during inflation and so ``tilts'' the primeval mass fluctuation spectrum of the CDM. The functional forms for the potentials and the parameter values that lead to an observationally acceptable model for structure formation do not seem to be out of line with current ideas about the physics of the very early universe. I argue in an accompanying paper that the model offers an acceptable fit to main observational constraints.Comment: 11 pages, 3 postscript figures, uses aas2pp4.st

A fit of the angular 3–point function and biased galaxy formation

A study of the 3-point function, based on the analysis of momenta (as was done, e.g., in Sharp et.al. 1984) deduced from the Zwicky catalog, indicates that an expression containing a cubic term, besides the usual second degree polynomials of 2–point functions, provides a good fit of angular data

Constraints on Inflationary Solutions in the Presence of Shear and Bulk Viscosity

Inflationary models and their claim to solve many of the outstanding problems in cosmology have been the subject of a great deal of debate over the last few years. A major sticking point has been the lack of both good observational and theoretical arguments to single out one particular model out of the many that solve these problems. Here we examine the degree of restrictiveness on the dynamical relationship between the cosmological scale factor and the inflation driving self-interaction potential of a minimally coupled scalar field, imposed by the condition that the scalar field is required to be real during a classical regime (the reality condition). We systema\-tically look at the effects of this constraint on many of the inflationary models found in the literature within the FLRW framework, and also look at what happens when physically motivated perturbations such as shear and bulk viscosity are introduced. We find that in many cases, either the models are totally excluded or the reality condition gives rise to constraints on the scale factor and on the various parameters of the model.Comment: 21 pages, LaTe