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Register a new userGalactos: Computing the Anisotropic 3-Point Correlation Function for 2 Billion Galaxies
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The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random distribution of galaxies. However, the 3PCFs formidable computational expense has prevented its application to astronomical surveys comprising millions to billions of galaxies. We present Galactos, a high-performance implementation of a novel, O(N^2) algorithm that uses a load-balanced k-d tree and spherical harmonic expansions to compute the anisotropic 3PCF. Our implementation is optimized for the Intel Xeon Phi architecture, exploiting SIMD parallelism, instruction and thread concurrency, and significant L1 and L2 cache reuse, reaching 39% of peak performance on a single node. Galactos scales to the full Cori system, achieving 9.8PF (peak) and 5.06PF (sustained) across 9636 nodes, making the 3PCF easily computable for all galaxies in the observable universe.
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We present the integrated 3-point shear correlation function $izeta_{pm}$ -- a higher-order statistic of the cosmic shear field -- which can be directly estimated in wide-area weak lensing surveys without measuring the full 3-point shear correlation function, making this a practical and complementary tool to 2-point statistics for weak lensing cosmology. We define it as the 1-point aperture mass statistic $M_{mathrm{ap}}$ measured at different locations on the shear field correlated with the corresponding local 2-point shear correlation function $xi_{pm}$. Building upon existing work on the integrated bispectrum of the weak lensing convergence field, we present a theoretical framework for computing the integrated 3-point function in real space for any projected field within the flat-sky approximation and apply it to cosmic shear. Using analytical formulae for the non-linear matter power spectrum and bispectrum, we model $izeta_{pm}$ and validate it on N-body simulations within the uncertainties expected from the sixth year cosmic shear data of the Dark Energy Survey. We also explore the Fisher information content of $izeta_{pm}$ and perform a joint analysis with $xi_{pm}$ for two tomographic source redshift bins with realistic shape-noise to analyse its power in constraining cosmological parameters. We find that the joint analysis of $xi_{pm}$ and $izeta_{pm}$ has the potential to considerably improve parameter constraints from $xi_{pm}$ alone, and can be particularly useful in improving the figure of merit of the dynamical dark energy equation of state parameters from cosmic shear data.
We present the Multiscale Coupling Library and Environment: MUSCLE 2. This multiscale component-based execution environment has a simple to use Java, C++, C, Python and Fortran API, compatible with MPI, OpenMP and threading codes. We demonstrate its local and distributed computing capabilities and compare its performance to MUSCLE 1, file copy, MPI, MPWide, and GridFTP. The local throughput of MPI is about two times higher, so very tightly coupled code should use MPI as a single submodel of MUSCLE 2; the distributed performance of GridFTP is lower, especially for small messages. We test the performance of a canal system model with MUSCLE 2, where it introduces an overhead as small as 5% compared to MPI.
The increasingly large amount of cosmological data coming from ground-based and space-borne telescopes requires highly efficient and fast enough data analysis techniques to maximise the scientific exploitation. In this work, we explore the capabilities of supervised machine learning algorithms to learn the properties of the large-scale structure of the Universe, aiming at constraining the matter density parameter, Omega m. We implement a new Artificial Neural Network for a regression data analysis, and train it on a large set of galaxy two-point correlation functions in standard cosmologies with different values of Omega m. The training set is constructed from log-normal mock catalogues which reproduce the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxies. The presented statistical method requires no specific analytical model to construct the likelihood function, and runs with negligible computational cost, after training. We test this new Artificial Neural Network on real BOSS data, finding Omega m=0.309p/m0.008, which is remarkably consistent with standard analysis results.
We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects. Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle. By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off $(k_{text{IR}} leq H_0)$ in computing the gravitational potential contribution. Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge. We find that the terms at the observer position such as the coordinate lapses and the observer velocity (missing in the standard formalism) dominate over the other relativistic contributions in the conformal Newtonian gauge such as the source velocity, the gravitational potential, the integrated Sachs-Wolf effect, the Shapiro time-delay and the lensing convergence. Compared to the standard Newtonian theoretical predictions that consider only the density fluctuation and redshift-space distortions, the relativistic effects in galaxy clustering result in a few percent-level systematic errors beyond the scale of the baryonic acoustic oscillation. Our theoretical and numerical study provides a comprehensive understanding of the relativistic effects in the galaxy two-point correlation function, as it proves the validity of the theoretical prediction and accounts for effects that are often neglected in its numerical evaluation.
We present an $8.1sigma$ detection of the non-Gaussian 4-Point Correlation Function (4PCF) using a sample of $N_{rm g} approx 8times 10^5$ galaxies from the BOSS CMASS dataset. Our measurement uses the $mathcal{O}(N_{rm g}^2)$ NPCF estimator of Philcox et al. (2021), including a new modification to subtract the disconnected 4PCF contribution (arising from the product of two 2PCFs) at the estimator level. This approach is unlike previous work and ensures that our signal is a robust detection of gravitationally-induced non-Gaussianity. The estimator is validated with a suite of lognormal simulations, and the analytic form of the disconnected contribution is discussed. Due to the high dimensionality of the 4PCF, data compression is required; we use a signal-to-noise-based scheme calibrated from theoretical covariance matrices to restrict to $sim$ $100$ basis vectors. The compression has minimal impact on the detection significance and facilitates traditional $chi^2$-like analyses using a suite of mock catalogs. The significance is stable with respect to different treatments of noise in the sample covariance (arising from the limited number of mocks), but decreases to $4.7sigma$ when a minimum galaxy separation of $14 h^{-1}mathrm{Mpc}$ is enforced on the 4PCF tetrahedra (such that the statistic can be modelled more easily). The detectability of the 4PCF in the quasi-linear regime implies that it will become a useful tool in constraining cosmological and galaxy formation parameters from upcoming spectroscopic surveys.
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