Constraining Scale-Dependent Non-Gaussianity with Future Large-Scale Structure and the CMB

We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f_NL is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f_NL(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f_NL(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussianity.Comment: 28 pages, 8 figures, 2 tables; v2: references update

Angpow: a software for the fast computation of accurate tomographic power spectra

The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular the matter power spectrum $P(k)$ brings information about the cosmological distance evolution and the galaxy clustering together. However the building of $P(k)$ from galaxy catalogues needs a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted $P(k)$ from other cosmological models, and for photometric surveys like LSST. The angular power spectrum $C_\ell(z_1,z_2)$ between two bins located at redshift $z_1$ and $z_2$ contains the same information than the matter power spectrum, is free from any cosmological assumption, but the prediction of $C_\ell(z_1,z_2)$ from $P(k)$ is a costly computation when performed exactly. The Angpow software aims at computing quickly and accurately the auto ($z_1=z_2$) and cross ($z_1 \neq z_2$) angular power spectra between redshift bins. We describe the developed algorithm, based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Angpow is flexible and can handle any user defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the $C_\ell(z_1,z_2)$ comparison with data. We emphasize that the Limber's approximation, often used to fasten the computation, gives wrong $C_\ell$ values for cross-correlations.Comment: Published in Astronomy & Astrophysic

A new model for the full shape of the large-scale power spectrum

We present a new model for the full shape of large-scale the power spectrum based on renormalized perturbation theory. To test the validity of this prescription, we compare this model against power spectra measured in a suite of 50 large volume, moderate resolution N-body simulations. Our results indicate that this simple model provides an accurate description of the full shape of the power spectrum taking into account the effects of non-linear evolution, redshift-space distortions and halo bias for scales k < 0.15 h/Mpc, making it a valuable tool for the analysis of forthcoming galaxy surveys. Even though its application is restricted to large scales, this prescription can provide tighter constraints on the dark energy equation of state parameter w_{DE} than those obtained by modelling the baryonic acoustic oscillations signal only, where the information of the broad-band shape of the power spectrum is discarded. Our model is able to provide constraints comparable to those obtained by applying a similar model to the full shape of the correlation function, which is affected by different systematics. Hence, with accurate modelling of the power spectrum, the same cosmological information can be extracted from both statistics.Comment: Accepted for publication in MNRA

On Approximating the Number of kk-cliques in Sublinear Time

We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let $n$ denote the number of vertices in the graph, $m$ the number of edges, and $C_k$ the number of $k$-cliques. We design an algorithm that outputs a $(1+\varepsilon)$-approximation (with high probability) for $C_k$, whose expected query complexity and running time are O\left(\frac{n}{C_k^{1/k}}+\frac{m^{k/2}}{C_k}\right)\poly(\log n,1/\varepsilon,k). Hence, the complexity of the algorithm is sublinear in the size of the graph for $C_k = \omega(m^{k/2-1})$. Furthermore, we prove a lower bound showing that the query complexity of our algorithm is essentially optimal (up to the dependence on $\log n$, $1/\varepsilon$ and $k$). The previous results in this vein are by Feige (SICOMP 06) and by Goldreich and Ron (RSA 08) for edge counting ($k=2$) and by Eden et al. (FOCS 2015) for triangle counting ($k=3$). Our result matches the complexities of these results. The previous result by Eden et al. hinges on a certain amortization technique that works only for triangle counting, and does not generalize for larger cliques. We obtain a general algorithm that works for any $k\geq 3$ by designing a procedure that samples each $k$-clique incident to a given set $S$ of vertices with approximately equal probability. The primary difficulty is in finding cliques incident to purely high-degree vertices, since random sampling within neighbors has a low success probability. This is achieved by an algorithm that samples uniform random high degree vertices and a careful tradeoff between estimating cliques incident purely to high-degree vertices and those that include a low-degree vertex

Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering

We perform an ensemble of $N$-body simulations with $2048^3$ particles for 101 flat $w$CDM cosmological models sampled based on a maximin-distance Sliced Latin Hypercube Design. By using the halo catalogs extracted at multiple redshifts in the range of $z=[0,1.48]$, we develop Dark Emulator, which enables fast and accurate computations of the halo mass function, halo-matter cross-correlation, and halo auto-correlation as a function of halo masses, redshift, separations and cosmological models, based on the Principal Component Analysis and the Gaussian Process Regression for the large-dimensional input and output data vector. We assess the performance of the emulator using a validation set of $N$-body simulations that are not used in training the emulator. We show that, for typical halos hosting CMASS galaxies in the Sloan Digital Sky Survey, the emulator predicts the halo-matter cross correlation, relevant for galaxy-galaxy weak lensing, with an accuracy better than $2\%$ and the halo auto-correlation, relevant for galaxy clustering correlation, with an accuracy better than $4\%$. We give several demonstrations of the emulator. It can be used to study properties of halo mass density profiles such as the mass-concentration relation and splashback radius for different cosmologies. The emulator outputs can be combined with an analytical prescription of halo-galaxy connection such as the halo occupation distribution at the equation level, instead of using the mock catalogs, to make accurate predictions of galaxy clustering statistics such as the galaxy-galaxy weak lensing and the projected correlation function for any model within the $w$CDM cosmologies, in a few CPU seconds.Comment: 46 pages, 47 figures; version accepted for publication in Ap

The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9

We present precise measurements of the growth rate of cosmic structure for the redshift range 0.1 < z < 0.9, using redshift-space distortions in the galaxy power spectrum of the WiggleZ Dark Energy Survey. Our results, which have a precision of around 10% in four independent redshift bins, are well-fit by a flat LCDM cosmological model with matter density parameter Omega_m = 0.27. Our analysis hence indicates that this model provides a self-consistent description of the growth of cosmic structure through large-scale perturbations and the homogeneous cosmic expansion mapped by supernovae and baryon acoustic oscillations. We achieve robust results by systematically comparing our data with several different models of the quasi-linear growth of structure including empirical models, fitting formulae calibrated to N-body simulations, and perturbation theory techniques. We extract the first measurements of the power spectrum of the velocity divergence field, P_vv(k), as a function of redshift (under the assumption that P_gv(k) = -sqrt[P_gg(k) P_vv(k)] where g is the galaxy overdensity field), and demonstrate that the WiggleZ galaxy-mass cross-correlation is consistent with a deterministic (rather than stochastic) scale-independent bias model for WiggleZ galaxies for scales k < 0.3 h/Mpc. Measurements of the cosmic growth rate from the WiggleZ Survey and other current and future observations offer a powerful test of the physical nature of dark energy that is complementary to distance-redshift measures such as supernovae and baryon acoustic oscillations.Comment: 17 pages, 11 figures, accepted for publication by MNRA