A local bias approach to the clustering of discrete density peaks

Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering statistics of discrete density peaks are difficult to evaluate. For this reason, local bias schemes have received considerably more attention in the literature thus far. In this paper, we show that the 2-point correlation function of maxima of a homogeneous and isotropic Gaussian random field can be thought of, up to second order at least, as arising from a local bias expansion formulated in terms of rotationally invariant variables. This expansion relies on a unique smoothing scale, which is the Lagrangian radius of dark matter halos. The great advantage of this local bias approach is that it circumvents the difficult computation of joint probability distributions. We demonstrate that the bias factors associated with these rotational invariants can be computed using a peak-background split argument, in which the background perturbation shifts the corresponding probability distribution functions. Consequently, the bias factors are orthogonal polynomials averaged over those spatial locations that satisfy the peak constraint. In particular, asphericity in the peak profile contributes to the clustering at quadratic and higher order, with bias factors given by generalized Laguerre polynomials. We speculate that our approach remains valid at all orders, and that it can be extended to describe clustering statistics of any point process of a Gaussian random field. Our results will be very useful to model the clustering of discrete tracers with more realistic collapse prescriptions involving the tidal shear for instance.Comment: 14 pages, 1 figure. (v2): typos fixed + references added. Accepted for publication in PR

Primordial non-Gaussianity in the large scale structure of the Universe

Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of significant non-Gaussianity would thus have profound implications for our understanding of cosmic structure formation. The large scale mass distribution in the Universe is a sensitive probe of the nature of initial conditions. Recent theoretical progress together with rapid developments in observational techniques will enable us to critically confront predictions of inflationary scenarios and set constraints as competitive as those from the Cosmic Microwave Background. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.Comment: 24 pages, 10 figures. To appear in the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" of Advances in Astronom

Joint modeling of the probability distribution and power spectrum of the Lya forest: comparison with observations at z=3

We presents results of joint modeling of the probability distribution function (PDF) and the one-dimensional power spectrum (PS) of the Lya forest flux decrement. The sensitivity of these statistical measures to the shape and amplitude of the linear matter power spectrum is investigated using two variants of the LCDM cosmology. In the first model, the linear power spectrum has a scale-invariant spectral index, whereas in the second, it has a negative running index (RSI). We generate mock catalogs of QSO spectra, and compare their statistical properties to those of the observations at z=3. We perform a joint fit of the power spectrum and PDF. A scale-invariant model with \sigma_8=0.9 matches well the data if the mean IGM temperature is T\leq 15000K. For higher temperature, it tends to overestimate the flux power spectrum over scales k < 0.01s/km. The discrepancy is less severe when the PS alone is fitted. However, models matching the PS alone do not yield a good fit to the PDF. A joint analysis of the flux PS and PDF tightens the constraints on the model parameters and reduces systematic biases. The RSI model is consistent with the observed PS and PDF only if the temperature is T\geq 20000K. The best fit models reproduce the slope and normalisation of the column density distribution, irrespective of the shape and amplitude of the linear power spectrum. They are also consistent with the observed line-width distribution given the large uncertainties. Our joint analysis suggests that \sigma_8 is likely to be in the range 0.7 - 0.9 for a temperature 10000K<T<20000K and a reasonable reionization history.Comment: revised version. new section discussing the impact of the PDF covariance matrix on the results. new figure comparing the constraints on sigma_8 obtained from the PS data alone, and from the PS+PDF. other minor changes. accepted for publication in MNRA

Signature of primordial non-Gaussianity of phi^3-type in the mass function and bias of dark matter haloes

We explore the effect of a cubic correction gnl*phi^3 on the mass function and bias of dark matter haloes extracted from a series of large N-body simulations and compare it to theoretical predictions. Such cubic terms can be motivated in scenarios like the curvaton model, in which a large cubic correction can be produced while simultaneously keeping the quadratic fnl*phi^2 correction small. The deviation from the Gaussian halo mass function is in reasonable agreement with the theoretical predictions. The scale-dependent bias correction Delta b_kappa(k,gnl) measured from the auto- and cross-power spectrum of haloes, is similar to the correction in fnl models, but the amplitude is lower than theoretical expectations. Using the compilation of LSS data in Slosar et al. (2008), we obtain for the first time a limit on gnl of -3.5*10^5 < gnl < +8.2*10^5 (at 95% CL). This limit will improve with the future LSS data by 1-2 orders of magnitude, which should test many of the scenarios of this type.Comment: 21 pages, 11 figures (v2): typo corrected, clarifications+references added (v3): paper somewhat reorganized, added discussion on initial conditions, version accepted by PR

Primordial non-Gaussianity from the large scale structure

Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generated the cosmological fluctuations observed today. Any detection of non-Gaussianity would have profound implications for our understanding of cosmic structure formation. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large scale structure of the Universe.Comment: Invited review article for the CQG special issue on nonlinear cosmological perturbations