The Real and Redshift Space Density Distribution Function for Large-Scale Structure in the Spherical Collapse Approximation

We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the $p$-order hierarchical amplitudes $S_p$, in both real and redshift space. We compare our results with numerical simulations, focusing on the $\Omega=1$ standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for \sigma_L \simgt 1, where $\sigma_L$ is the linearly-evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for \sigma_L \simlt 0.4. Numerical simulations also yield a simple empirical relation between the real-space PDF and redshift-space PDF: we find that for \sigma \simlt 1, the redshift space PDF, P[\delta_z], is, to a good approximation, a simple rescaling of the real space PDF, P[\delta], i.e., P[\delta/\sigma] d[\delta/\sigma] = P[\delta_z/\sigma_z] d[\delta_z/\sigma_z], where $\sigma$ and \sigma_z are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the Lambda-CDM model. It breaks down for SCDM at $\sigma \approx 1$, but provides a good fit to the \Lambda-CDM models for $\sigma$ as large as 0.8.Comment: 9 pages, latex, 12 figures added (26 total), minor changes to conclusions, to appear in MNRA

Cross-Correlation of spectroscopic and photometric galaxy surveys: cosmology from lensing and redshift distortions

Cosmological galaxy surveys aim at mapping the largest volumes to test models with techniques such as cluster abundance, cosmic shear correlations or baryon acoustic oscillations (BAO), which are designed to be independent of galaxy bias. Here we explore an alternative route to constrain cosmology: sampling more moderate volumes with the cross-correlation of photometric and spectroscopic surveys. We consider the angular galaxy-galaxy autocorrelation in narrow redshift bins and its combination with different probes of weak gravitational lensing (WL) and redshift space distortions (RSD). Including the cross-correlation of these surveys improves by factors of a few the constraints on both the dark energy equation of state w(z) and the cosmic growth history, parametrized by \gamma. The additional information comes from using many narrow redshift bins and from galaxy bias, which is measured both with WL probes and RSD, breaking degeneracies that are present when using each method separately. We show forecasts for a joint w(z) and \gamma figure of merit using linear scales over a deep (i<24) photometric survey and a brighter (i<22.5) spectroscopic or very accurate (0.3%) photometric redshift survey. Magnification or shear in the photometric sample produce FoM that are of the same order of magnitude of those of RSD or BAO over the spectroscopic sample. However, the cross-correlation of these probes over the same area yields a FoM that is up to a factor 100 times larger. Magnification alone, without shape measurements, can also be used for these cross-correlations and can produce better results than using shear alone. For a spectroscopic follow-up survey strategy, measuring the spectra of the foreground lenses to perform this cross-correlation provides 5 times better FoM than targeting the higher redshift tail of the galaxy distribution to study BAO over a 2.5 times larger volume.Comment: Small cosmetic changes to match MNRAS published versio

Constraining neutrino masses with the ISW-galaxy correlation function

Temperature anisotropies in the Cosmic Microwave Background (CMB) are affected by the late Integrated Sachs-Wolfe (lISW) effect caused by any time-variation of the gravitational potential on linear scales. Dark energy is not the only source of lISW, since massive neutrinos induce a small decay of the potential on small scales during both matter and dark energy domination. In this work, we study the prospect of using the cross-correlation between CMB and galaxy density maps as a tool for constraining the neutrino mass. On the one hand massive neutrinos reduce the cross-correlation spectrum because free-streaming slows down structure formation; on the other hand, they enhance it through their change in the effective linear growth. We show that in the observable range of scales and redshifts, the first effect dominates, but the second one is not negligible. We carry out an error forecast analysis by fitting some mock data inspired by the Planck satellite, Dark Energy Survey (DES) and Large Synoptic Survey Telescope (LSST). The inclusion of the cross-correlation data from Planck and LSST increases the sensitivity to the neutrino mass m_nu by 38% (and to the dark energy equation of state w by 83%) with respect to Planck alone. The correlation between Planck and DES brings a far less significant improvement. This method is not potentially as good for detecting m_nu as the measurement of galaxy, cluster or cosmic shear power spectra, but since it is independent and affected by different systematics, it remains potentially interesting if the total neutrino mass is of the order of 0.2 eV; if instead it is close to the lower bound from atmospheric oscillations, m_nu ~ 0.05 eV, we do not expect the ISW-galaxy correlation to be ever sensitive to m_nu.Comment: 10 pages, 8 figures. References added. Accepted for publication in Phys.Rev.

Halo Sampling, Local Bias and Loop Corrections

We develop a new test of local bias, by constructing a locally biased halo density field from sampling the dark matter-halo distribution. Our test differs from conventional tests in that it preserves the full scatter in the bias relation and it does not rely on perturbation theory. We put forward that bias parameters obtained using a smoothing scale R can only be applied to computing the halo power spectrum at scales k ~ 1/R. Our calculations can automatically include the running of bias parameters and give vanishingly small loop corrections at low-k. Our proposal results in much better agreement of the sampling and perturbation theory results with simulations. In particular, unlike the standard interpretation of local bias in the literature, our treatment of local bias does not generate a constant power in the low-k limit. We search for extra noise in the Poisson corrected halo power spectrum at wavenumbers below its turn-over and find no evidence of significant positive noise (as predicted by the standard interpretation) while we find evidence of negative noise coming from halo exclusion for very massive halos. Using perturbation theory and our non-perturbative sampling technique we also demonstrate that nonlocal bias effects discovered recently in simulations impact the power spectrum only at the few percent level in the weakly nonlinear regime.Comment: 25 pages, 14 figures; V2: significant revision including more details about halo exclusion and low-k noise. Conclusions unchange

Skewness as a probe of non-Gaussian initial conditions

We compute the skewness of the matter distribution arising from non-linear evolution and from non-Gaussian initial perturbations. We apply our result to a very generic class of models with non-Gaussian initial conditions and we estimate analytically the ratio between the skewness due to non-linear clustering and the part due to the intrinsic non-Gaussianity of the models. We finally extend our estimates to higher moments.Comment: 5 pages, 2 ps-figs., accepted for publication in PRD, rapid com

Statistical analysis of galaxy surveys — II. The three-point galaxy correlation function measured from the 2dFGRS

We present new results for the three-point correlation function, ζ, measured as a function of scale, luminosity and colour from the final version of the 2dF Galaxy Redshift Survey (2dFGRS). The reduced three-point correlation function, Q3~ζ/ξ2, is estimated for different triangle shapes and sizes, employing a full covariance analysis. The form of Q3 is consistent with the expectations for the Λ cold dark matter model, confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations. However, we find a clear offset in amplitude between Q3 for galaxies and the predictions for the dark matter. We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9σ level. On weakly non-linear scales, we can interpret our results in terms of galaxy bias parameters. We find a linear bias term that is consistent with unity, b1= 0.93+0.10-0.08 and a quadratic bias c2=b2/b1=-0.34+0.11-0.08. This is the first significant detection of a non-zero quadratic bias, indicating a small but important non-gravitational contribution to the three-point function. Our estimate of the linear bias from the three-point function is independent of the normalization of underlying density fluctuations, so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations. We find that the rms linear theory variance in spheres of radius 8 h−1 Mpc is σ8= 0.88+0.12-0.10, providing an independent confirmation of values derived from other techniques. On non-linear scales, where ξ > 1, we find that Q3 has a strong dependence on scale, colour and luminosit

The 3-point function in the large scale structure: I. The weakly non-linear regime in N-body simulations

This paper presents a comparison of the predictions for the 2 and 3-point correlation functions of density fluctuations, xi_2 and xi_3, in gravitational perturbation theory (PT) against large Cold Dark Matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10 Mpc/h) thanks to the development of a new algorithm to estimate correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the 3-point statistics to simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as the ones presented here, were limited to small scales were leading order PT gives a poor approximation. Here we also propose and apply a method for separating the first and subsequent orders contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime were simulations do reproduce the leading order (tree-level) predictions of PT for the reduced 3-point function Q_3 ~ xi_3/ xi_2^2. For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ~ 20 Mpc/h. On larger scales xi_2 goes to zero and the results are dominated by sampling errors. In more realistic models (like the Lambda CDM cosmology) deviations from the leading order PT become important at smaller scales ~ 10 Mpc/h, although this depends on the particular 3-point configuration. (abridge)Comment: 12 pages, 9 figures, minor changes. Final version accepted for publication in MNRA