Non Gaussian Minkowski functionals and extrema counts for 2D sky maps

In the conference presentation we have reviewed the theory of non-Gaussian geometrical measures for the 3D Cosmic Web of the matter distribution in the Universe and 2D sky data, such as Cosmic Microwave Background (CMB) maps that was developed in a series of our papers. The theory leverages symmetry of isotropic statistics such as Minkowski functionals and extrema counts to develop post- Gaussian expansion of the statistics in orthogonal polynomials of invariant descriptors of the field, its first and second derivatives. The application of the approach to 2D fields defined on a spherical sky was suggested, but never rigorously developed. In this paper we present such development treating effects of the curvature and finiteness of the spherical space $S_2$ exactly, without relying on the flat-sky approximation. We present Minkowski functionals, including Euler characteristic and extrema counts to the first non-Gaussian correction, suitable for weakly non-Gaussian fields on a sphere, of which CMB is the prime example.Comment: 6 pages, to appear as proceedings of the IAU Symposium No. 308, 2014 The Zeldovich Universe, Genesis and Growth of the Cosmic Web Rien van de Weygaert, Sergei Shandarin, Enn Saar and Jaan Einast

Statistics of cosmic density profiles from perturbation theory

The joint probability distribution function (PDF) of the density within multiple concentric spherical cells is considered. It is shown how its cumulant generating function can be obtained at tree order in perturbation theory as the Legendre transform of a function directly built in terms of the initial moments. In the context of the upcoming generation of large-scale structure surveys, it is conjectured that this result correctly models such a function for finite values of the variance. Detailed consequences of this assumption are explored. In particular the corresponding one-cell density probability distribution at finite variance is computed for realistic power spectra, taking into account its scale variation. It is found to be in agreement with $\Lambda$-CDM simulations at the few percent level for a wide range of density values and parameters. Related explicit analytic expansions at the low and high density tails are given. The conditional (at fixed density) and marginal probability of the slope -- the density difference between adjacent cells -- and its fluctuations is also computed from the two-cells joint PDF; it also compares very well to simulations, in particular in under-dense regions, with a significant reduced cosmic scatter compared to over-dense regions. It is emphasized that this could prove useful when studying the statistical properties of voids as it can serve as a statistical indicator to test gravity models and/or probe key cosmological parameters.Comment: 22 pages, 15 figures, submitted to PR

Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity

The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function of peaks of a given height is numerically estimated and analytical approximations that are valid inside the exclusion zone are derived. The resulting power spectrum of these tracers is investigated and shows clear deviations from Poisson noise at low frequencies. On large scales, the convergence of a perturbative bias expansion is discussed. Finally, we go beyond Gaussian statistics for the initial conditions and investigate the subsequent evolution of the two-point clustering of peaks through their Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with scale-dependencies induced by nonlinear gravitational evolution. While the expected large-scale separation limit is recovered, significant deviations are found in the exclusion zone that tends in particular to be reduced at later times. Even though these findings apply to the clustering of one-dimensional tracers, they provide useful insights into halo exclusion and its impact on the two-halo term.Comment: 16 pages, 9 figures, accepted for publication in MNRA

Encircling the dark: constraining dark energy via cosmic density in spheres

The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few percent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical collapse dynamics is made available online so as to provide straightforward means of testing the effect of alternative dark energy models and initial power-spectra on the low-redshift matter distribution.Comment: 7 pages, replaced to match the MNRAS accepted versio

The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when predicting the generating function of cumulants containing any powers of concentric densities in one location and one power of density at some arbitrary distance from the rest. This exact "one external leg" cumulant generating function is used in particular to probe the rate of convergence of the large-separation approximation.Comment: 17 pages, 10 figures, replaced to match the MNRAS accepted versio

Non-Gaussian Minkowski functionals & extrema counts in redshift space

In the context of upcoming large-scale structure surveys such as Euclid, it is of prime importance to quantify the effect of peculiar velocities on geometric probes. Hence the formalism to compute in redshift space the geometrical and topological one-point statistics of mildly non-Gaussian 2D and 3D cosmic fields is developed. Leveraging the partial isotropy of the target statistics, the Gram-Charlier expansion of the joint probability distribution of the field and its derivatives is reformulated in terms of the corresponding anisotropic variables. In particular, the cosmic non-linear evolution of the Minkowski functionals, together with the statistics of extrema are investigated in turn for 3D catalogues and 2D slabs. The amplitude of the non-Gaussian redshift distortion correction is estimated for these geometric probes. In 3D, gravitational perturbation theory is implemented in redshift space to predict the cosmic evolution of all relevant Gram-Charlier coefficients. Applications to the estimation of the cosmic parameters sigma(z) and beta=f/b1 from upcoming surveys is discussed. Such statistics are of interest for anisotropic fields beyond cosmology.Comment: 35 pages, 15 figures, matches version published in MNRAS with a typo corrected in eq A1

RegPT: Direct and fast calculation of regularized cosmological power spectrum at two-loop order

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory (PT), based on the multi-point propagator expansion. In this approach power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-k limit and the standard PT results at low-k. With the help of N-body simulations, we show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent-level in the weakly non-linear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of pre-computed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum cosmic emulator from which a wide variety of cosmological models can be explored. The fortran program with which direct and fast calculations of power spectra can be done, RegPT, is publicly released as part of this paper.Comment: 28 pages, 15 figure

How the cosmic web induces intrinsic alignments of galaxies

Intrinsic alignments are believed to be a major source of systematics for future generation of weak gravitational lensing surveys like Euclid or LSST. Direct measurements of the alignment of the projected light distribution of galaxies in wide field imaging data seem to agree on a contamination at a level of a few per cent of the shear correlation functions, although the amplitude of the effect depends on the population of galaxies considered. Given this dependency, it is difficult to use dark matter-only simulations as the sole resource to predict and control intrinsic alignments. We report here estimates on the level of intrinsic alignment in the cosmological hydrodynamical simulation Horizon-AGN that could be a major source of systematic errors in weak gravitational lensing measurements. In particular, assuming that the spin of galaxies is a good proxy for their ellipticity, we show how those spins are spatially correlated and how they couple to the tidal field in which they are embedded. We also present theoretical calculations that illustrate and qualitatively explain the observed signals.Comment: 6 pages, contribution to the proceedings of IAU Symposium 308 "The Zeldovich Universe: Genesis and Growth of the Cosmic Web

Caught in the rhythm II: Competitive alignments of satellites with their inner halo and central galaxy

The anisotropic distribution of satellites around the central galaxy of their host halo is well-documented. However the relative impact of baryons and dark matter in shaping this distribution is still debated. Using the simulation Horizon-AGN, the angular distribution of satellite galaxies with respect to their central counterpart and halo is quantified. Below one Rvir, satellites cluster more strongly in the plane of the central, rather than merely tracing the shape of their host halo. This is due to the increased isotropy of inner haloes acquired through their inside-out assembly in vorticity-rich flows along the cosmic web. While the effect of centrals decreases with distance, halos' triaxiality increases, impacting more and more the satellite's distribution. Effects become comparable just outside one virial radius. Above this scale, the filamentary infall also impacts the satellites distribution, dominating above two virial radii. The central's morphology plays a governing role: the alignment w.r.t. the central plane is four times stronger in haloes hosting stellar discs than in spheroids. But the impact of the galactic plane decreases for lower satellite-to-central mass ratios, suggesting this might not hold for dwarf satellites of the Local group. The orientation of the Milky-Way's satellites traces their cosmic filament, their level of coplanarity is consistent with systems of similar mass and cosmic location in Horizon-AGN. However, the strong impact of galactic planes in massive groups and clusters bounds the likelihood of finding a relaxed region where satellites can be used to infer halo shape. The minor-to-major axis ratios for haloes with log(M0/Msun)>13.5 is underestimated by 10%. This error soars quickly to 30-40% for individual halo measurements.Comment: 30 pages, 28 figures, submitted to A&

Intrinsic alignment of simulated galaxies in the cosmic web: implications for weak lensing surveys

The intrinsic alignment of galaxy shapes (by means of their angular momentum) and their cross-correlation with the surrounding dark matter tidal field are investigated using the 160 000, z=1.2 synthetic galaxies extracted from the high-resolution cosmological hydrodynamical simulation Horizon-AGN. One- and two-point statistics of the spin of the stellar component are measured as a function of mass and colour. For the low-mass galaxies, this spin is locally aligned with the tidal field `filamentary' direction while, for the high-mass galaxies, it is perpendicular to both filaments and walls. The bluest galaxies of our synthetic catalog are more strongly correlated with the surrounding tidal field than the reddest galaxies, and this correlation extends up to 10 Mpc/h comoving distance. We also report a correlation of the projected ellipticities of blue, intermediate mass galaxies on a similar scale at a level of 10^(-4) which could be a concern for cosmic shear measurements. We do not report any measurable intrinsic alignments of the reddest galaxies of our sample. This work is a first step toward the use of very realistic catalog of synthetic galaxies to evaluate the contamination of weak lensing measurement by the intrinsic galactic alignments.Comment: 15 pages, accepted for publication in MNRA