The effect of primordial non-Gaussianity on halo bias

It has long been known how to analytically relate the clustering properties of the collapsed structures (halos) to those of the underlying dark matter distribution for Gaussian initial conditions. Here we apply the same approach to physically motivated non-Gaussian models. The techniques we use were developed in the 1980s to deal with the clustering of peaks of non-Gaussian density fields. The description of the clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys. For inflationary-motivated non-Gaussianites, we find an analytic expression for the halo bias as a function of scale, mass and redshift, employing only the approximations of high-peaks and large separations.Comment: 4 pages, 3 figures, submitted. Typos fixed, reference added, minor clarifications in the tex

Non-Gaussian halo bias and future galaxy surveys

We forecast constraints on primordial non-Gaussianity achievable from forthcoming surveys by exploiting the scale-dependent halo bias introduced on large scales by non-Gaussian initial conditions. We explore the performance of exploiting both the shape of the galaxy power-spectrum on large scales and the cross-correlation of galaxies with Cosmic Microwave Background maps through the Integrated Sachs Wolfe effect. We find that future surveys can detect primordial non-Gaussianity of the local form with a non-Gaussianity parameter $|f_{\rm NL}|$ of order unity. This is particularly exciting because, while the simplest single-field slow-roll models of inflation predict a primordial $|f_{\rm NL}|\ll 1$, this signal sources extra contributions to the effective $f_{\rm NL}$ of large-scale structures that are expected to be above our predicted detection threshold.Comment: 5pages, 1 Table, typos correcte

Primordial Non-Gaussianity and the NRAO VLA Sky Survey

The NRAO VLA Sky Survey (NVSS) is the only dataset that allows an accurate determination of the auto-correlation function (ACF) on angular scales of several degrees for Active Galactic Nuclei (AGNs) at typical redshifts $z \simeq 1$. Surprisingly, the ACF is found to be positive on such large scales while, in the framework of the standard hierarchical clustering scenario with Gaussian primordial perturbations it should be negative for a redshift-independent effective halo mass of order of that found for optically-selected quasars. We show that a small primordial non-Gaussianity can add sufficient power on very large scales to account for the observed NVSS ACF. The best-fit value of the parameter $f_{\rm NL}$, quantifying the amplitude of primordial non-Gaussianity of local type is $f_{\rm NL}=62 \pm 27$ ($1\,\sigma$ error bar) and $25<f_{\rm NL}<117$ ($2\,\sigma$ confidence level), corresponding to a detection of non-Gaussianity significant at the $\sim 3\,\sigma$ confidence level. The minimal halo mass of NVSS sources is found to be $M_{\rm min}=10^{12.47\pm0.26}h^{-1}M_{\odot}$ ($1\,\sigma$) strikingly close to that found for optically selected quasars. We discuss caveats and possible physical and systematic effects that can impact on the results.Comment: 6 pages, 5 figure

Gravitational Wave Background from a Cosmological Population of Core-Collapse Supernovae

We analyse the stochastic background of gravitational radiation emitted by a cosmological population of core-collapse supernovae. The supernova rate as a function of redshift is deduced from an observation-based determination of the star formation rate density evolution. We then restrict our analysis to the range of progenitor masses leading to black hole collapse. In this case, the main features of the gravitational-wave emission spectra have been shown to be, to some extent, independent of the initial conditions and of the equation of state of the collapsing star, and to depend only on the black hole mass and angular momentum. We calculate the overall signal produced by the ensemble of black-hole collapses throughout the Universe, assuming a flat cosmology with vanishing cosmological constant. Within a wide range of parameter values, we find that the spectral strain amplitude has a maximum at a few hundred Hz with an amplitude between $10^{-28}$ and $10^{-27} Hz^{-1/2}$; the corresponding closure density, $\Omega_{GW}$, has a maximum amplitude ranging between $10^{-11}$ and $10^{-10}$ in the frequency interval $\sim 1.5-2.5$ kHz. Contrary to previous claims, our observation-based determination leads to a duty cycle of order 0.01, making our stochastic backgound a non-continuous one. Although the amplitude of our background is comparable to the sensitivity that can be reached by a pair of advanced LIGO detectors, the characteristic shot-noise structure of the predicted signal might be in principle exploited to design specific detection strategies.Comment: 12 pages, LaTeX (uses mn.sty), 13 figures, 2 tables, accepted for publication in MNRA

Extended Quintessence: imprints on the cosmic microwave background spectra

We describe the observable features of the recently proposed Extended Quintessence scenarios on the Cosmic Microwave Background (CMB) anisotropy spectra. In this class of models a scalar field $\phi$, assumed to provide most of the cosmic energy density today, is non-minimally coupled to the Ricci curvature scalar $R$. We implement the linear theory of cosmological perturbations in scalar tensor gravitational theories to compute CMB temperature and polarization spectra. All the interesting spectral features are affected: on sub-degree angular scales, the acoustic peaks change both in amplitude and position; on larger scales the low redshift dynamics enhances the Integrated Sachs Wolfe effect. These results show how the future CMB experiments could give information on the vacuum energy as well as on the structure of the gravitational Lagrangian term.Comment: 4 pages including 1 figure, to be published in the proceedings of the COSMO99 meeting, held in Trieste, September 199

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 $\Omega$. 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.Comment: 40 pages with 4 figures, compressed and uuencoded PostScript file, submitted to ApJ, SISSA preprint Ref. 85/94/

Cosmic Microwave Background Anisotropies up to Second Order

These lecture notes present the computation of the full system of Boltzmann equations describing the evolution of the photon, baryon and cold dark matter fluids up to second order in perturbation theory, as recently studied in (Bartolo, Matarrese & Riotto 2006, 2007). These equations allow to follow the time evolution of the cosmic microwave background anisotropies at all angular scales from the early epoch, when the cosmological perturbations were generated, to the present, through the recombination era. The inclusion of second-order contributions is mandatory when one is interested in studying possible deviations from Gaussianity of cosmological perturbations, either of primordial (e.g. inflationary) origin or due to their subsequent evolution. Most of the emphasis in these lectures notes will be given to the derivation of the relevant equations for the study of cosmic microwave background anisotropies and to their analytical solutions.Comment: 53 pages, LaTeX file. Lectures given by S.M. at Les Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, Les Houches, France, 31 Jul - 25 Aug 2006. To appear in the Proceedings. Second version with minor misprints correcte

Post-Newtonian cosmological dynamics of plane-parallel perturbations and back-reaction

We study the general relativistic non-linear dynamics of self-gravitating irrotational dust in a cosmological setting, adopting the comoving and synchronous gauge, where all the equations can be written in terms of the metric tensor of spatial hyper-surfaces orthogonal to the fluid flow. Performing an expansion in inverse powers of the speed of light, we obtain the post-Newtonian equations, which yield the lowest-order relativistic effects arising during the non-linear evolution. We then specialize our analysis to globally plane-parallel configurations, i.e. to the case where the initial perturbation field depends on a single coordinate. The leading order of our expansion, corresponding to the "Newtonian background", is the Zel'dovich approximation, which, for plane-parallel perturbations in the Newtonian limit, represents an exact solution. This allows us to find the exact analytical form for the post-Newtonian metric, thereby providing the post-Newtonian extension of the Zel'dovich solution: this accounts for some relativistic effects, such as the non-Gaussianity of primordial perturbations. An application of our solution in the context of the back-reaction proposal is eventually given, providing a post-Newtonian estimation of kinematical back-reaction, mean spatial curvature and average scale-factor.Comment: revised to match the version accepted for publication in JCA

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