Cosmic Large Scale Structure Research Articles

Kinetic field theory: exact free evolution of Gaussian phase-space correlations

In recent work we developed a description of cosmic large-scale structure formation in terms of non-equilibrium ensembles of classical particles, with time evolution obtained in the framework of a statistical field theory. In these works, the initial correlations between particles sampled from random Gaussian density and velocity fields have so far been treated perturbatively or restricted to pure momentum correlations. Here we treat the correlations between all phase-space coordinates exactly by adopting a diagrammatic language for the different forms of correlations, directly inspired by the Mayer cluster expansion. We will demonstrate that explicit expressions for phase-space density cumulants of arbitrary n-point order, which fully capture the non-linear coupling of free streaming kinematics due to initial correlations, can be obtained from a simple set of Feynman rules. These cumulants will be the foundation for future investigations of perturbation theory in particle interactions.

Angular ellipticity correlations in a composite alignment model for elliptical and spiral galaxies and inference from weak lensing

We investigate a physical, composite alignment model for both spiral and elliptical galaxies and its impact on cosmological parameter estimation from weak lensing for a tomographic survey. Ellipticity correlation functions and angular ellipticity spectra for spiral and elliptical galaxies are derived on the basis of tidal interactions with the cosmic large-scale structure and compared to the tomographic weak lensing signal. We find that elliptical galaxies cause a contribution to the weak-lensing dominated ellipticity correlation on intermediate angular scales between $\ell\simeq40$ and $\ell\simeq400$ before that of spiral galaxies dominates on higher multipoles. The predominant term on intermediate scales is the negative cross-correlation between intrinsic alignments and weak gravitational lensing (GI-alignment). We simulate parameter inference from weak gravitational lensing with intrinsic alignments unaccounted; the bias induced by ignoring intrinsic alignments in a survey like Euclid is shown to be several times larger than the statistical error and can lead to faulty conclusions when comparing to other observations. The biases generally point into different directions in parameter space, such that in some cases one can observe a partial cancellation effect. Furthermore, it is shown that the biases increase with the number of tomographic bins used for the parameter estimation process. We quantify this parameter estimation bias in units of the statistical error and compute the loss of Bayesian evidence for a model due to the presence of systematic errors as well as the Kullback-Leibler divergence to quantify the distance between the true model and the wrongly inferred one.

Eddington's demon: inferring galaxy mass functions and other distributions from uncertain data

We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package "dftools" is equally applicable to other objects, such as haloes, groups and clusters, as well as observables other than mass. The formalism readily extends to multi-dimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasise the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.

The extended ROSAT-ESO Flux-Limited X-ray Galaxy Cluster Survey (REFLEX II)

The mass function of galaxy clusters is a sensitive tracer of the gravitational evolution of the cosmic large-scale structure and serves as an important census of the fraction of matter bound in large structures. We obtain the mass function by fitting the observed cluster X-ray luminosity distribution from the REFLEX galaxy cluster survey to models of cosmological structure formation. We marginalise over uncertainties in the cosmological parameters as well as those of the relevant galaxy cluster scaling relations. The mass function is determined with an uncertainty less than 10% in the mass range 3 x 10^12 to 5 x 10^14 M$_\odot$. For the cumulative mass function we find a slope at the low mass end consistent with a value of -1, while the mass rich end cut-off is milder than a Schechter function with an exponential term exp($- M^\delta$) with $\delta$ smaller than 1. Changing the Hubble parameter in the range $H_0 = 67 - 73 km s^-1 Mpc^{-1}$ or allowing the total neutrino mass to have a value between 0 - 0.4 eV causes variations less than the uncertainties. We estimate the fraction of mass locked up in galaxy clusters: about 4.4% of the matter in the Universe is bound in clusters (inside $r_200$) with a mass larger than 10^14 M$_\odot$ and 14% to clusters and groups with a mass larger than 10^13 M$_\odot$ at the present Universe. We also discuss the evolution of the galaxy cluster population with redshift. Our results imply that there is hardly any clusters with a mass > 10^15 M$_\odot$ above a redshift of z = 1.

Quantification of LSS using the persistent homology in the SDSS fields

Using galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12), we first estimate the topology of cosmic large-scale structure (LSS) by means of a new method of persistent homology which captures the size and robustness of the void structure in a compact and meaningful manner. To avoid cosmic variance, we create three volume-limited subsamples, which contain more than 2000 galaxies in different redshift slices (Δz=0.01). The result shows the clearer differences from the topology of uniform distribution as the redshift decreases, and supports the scenario of modern cosmology that the LSS has been formed through the growth in time of an initial density perturbation. Future work will include an analysis for different types of galaxies and a comparison with N-body simulation to constrain cosmological models.

How does the cosmic large-scale structure bias the Hubble diagram?

The Hubble diagram is one of the cornerstones of observational cosmology. It is usually analysed assuming that, on average, the underlying relation between magnitude and redshift matches the prediction of a Friedmann-Lemaître-Robertson-Walker model. However, the inhomogeneity of the Universe generically biases these observables, mainly due to peculiar velocities and gravitational lensing, in a way that depends on the notion of average used in theoretical calculations. In this article, we carefully derive the notion of average which corresponds to the observation of the Hubble diagram. We then calculate its bias at second-order in cosmological perturbations, and estimate the consequences on the inference of cosmological parameters, for various current and future surveys. We find that this bias deeply affects direct estimations of the evolution of the dark-energy equation of state. However, errors in the standard inference of cosmological parameters remain smaller than observational uncertainties, even though they reach percent level on some parameters; they reduce to sub-percent level if an optimal distance indicator is used.

The Cosmic Large-Scale Structure in X-rays (CLASSIX) Cluster Survey

To search for a signature of an intracluster magnetic field, we compare measurements of Faraday rotation of polarised extragalactic radio sources in the line of sight of galaxy clusters with those outside. To this end, we correlated a catalogue of 1383 rotation measures of extragalactic polarised radio sources with galaxy clusters from the CLASSIX survey (combining REFLEX II and NORAS II) detected by their X-ray emission in the ROSAT All-Sky Survey. The survey covers 8.25 ster of the sky at | bII | ≥ 20°. We compared the rotation measures in the line of sight of clusters within their projected radii of r500 with those outside and found a significant excess of the dispersion of the rotation measures in the cluster regions. Since the observed rotation measure is the result of Faraday rotation in several presumably uncorrelated magnetised cells of the intracluster medium, the observations correspond to quantities averaged over several magnetic field directions and strengths. Therefore the interesting quantity is the dispersion or standard deviation of the rotation measure for an ensemble of clusters. In the analysis of the observations we found a standard deviation of the rotation measure inside r500 of about 120 (± 21) rad m-2. This compares to about 56 (± 8) rad m-2 outside. Correcting for the effect of the Galaxy with the mean rotation measure in a region of 10 deg radius in the outskirts of the clusters does not change the outcome quoted above. We show that the most X-ray luminous and thus most massive clusters contribute most to the observed excess rotation measure. Modelling the electron density distribution in the intracluster medium with a self-similar model based on the REXCESS Survey, we found that the dispersion of the rotation measure increases with the column density, and we deduce a magnetic field value of about 2−6 (l/ 10 kpc)− 1/2μG assuming a constant magnetic field strength, where l is the size of the coherently magnetised intracluster medium cells. This magnetic field energy density amounts to a few percent of the average thermal energy density in clusters. On the other hand, when we allowed the magnetic field to vary such that the magnetic energy density is a constant fraction of the thermal energy density, we deduced a slightly lower value for this fraction of 3−10 (l/ 10 kpc)− 1/2 per mille. Compared to the situation in the Milky Way, where the ratio of the magnetic to thermal energy density is about unity, this ratio is much lower in galaxy clusters. The reason for this is most probably the different generation mechanism for the magnetic field, which is mostly powered by supernovae in the Galaxy and by turbulence from cluster mergers in galaxy clusters. The latter process sets a natural upper limit on the growth of the magnetic field.

A Fortunate Half-Century

The author has had the happy opportunity to work and study in the field of theoretical astrophysics during a half-century of unparalleled observational discovery. Quasars, pulsars, large-scale cosmic structure, galaxy evolution, and many other phenomena were discovered using revolutionary new observational techniques. In the same period of time, analytical tools ranging from new disciplines like plasma physics to enormously enhanced computational facilities became available, giving theoreticians the machinery to make some sense of this new world. At the start of the era the extragalactic world was largely framed as a quasi-homogeneous Universe of static galaxies formed by unknown and in fact unexamined processes. By the end of the period there was widespread acceptance of a self-consistent, evolving cosmological model amenable to calculation and comprehension. The author was fortunate indeed to have had the chance to collaborate with many wonderfully talented colleagues during this exciting time, attempting to unravel the multiple cosmic puzzles that nature delivered to us.

Constraints on neutrino masses from the study of the nearby large-scale structure and galaxy cluster counts

The high precision measurements of the cosmic microwave background by the Planck survey yielded tight constraints on cosmological parameters and the statistics of the density fluctuations at the time of recombination. This provides the means for a critical study of structure formation in the Universe by comparing the microwave background results with present epoch measurements of the cosmic large-scale structure. It can reveal subtle effects such as how different forms of Dark Matter may modify structure growth. Currently most interesting is the damping effect of structure growth by massive neutrinos. Different observations of low redshift matter density fluctuations provided evidence for a signature of massive neutrinos. Here we discuss the study of the cosmic large-scale structure with a complete sample of nearby, X-ray luminous clusters from our REFLEX cluster survey. From the observed X-ray luminosity function and its reproduction for different cosmological models, we obtain tight constraints on the cosmological parameters describing the matter density, [Formula: see text], and the density fluctuation amplitude, [Formula: see text]. A comparison of these constraints with the Planck results shows a discrepancy in the framework of a pure [Formula: see text]CDM model, but the results can be reconciled, if we allow for a neutrino mass in the range of 0.17 eV to 0.7 eV. Also some others, but not all of the observations of the nearby large-scale structure provide evidence or trends for signatures of massive neutrinos. With further improvement in the systematics and future survey projects, these indications will develop into a definitive measurement of neutrino masses.

Using rotation measure grids to detect cosmological magnetic fields: A Bayesian approach

Determining magnetic field properties in different environments of the cosmic large-scale structure as well as their evolution over redshift is a fundamental step toward uncovering the origin of cosmic magnetic fields. Radio observations permit the study of extragalactic magnetic fields via measurements of the Faraday depth of extragalactic radio sources. Our aim is to investigate how much different extragalactic environments contribute to the Faraday depth variance of these sources. We develop a Bayesian algorithm to distinguish statistically Faraday depth variance contributions intrinsic to the source from those due to the medium between the source and the observer. In our algorithm the Galactic foreground and the measurement noise are taken into account as the uncertainty correlations of the galactic model. Additionally, our algorithm allows for the investigation of possible redshift evolution of the extragalactic contribution. This work presents the derivation of the algorithm and tests performed on mock observations. With cosmic magnetism being one of the key science projects of the new generation of radio interferometers we have made predictions for the algorithm's performance on data from the next generation of radio interferometers. Applications to real data are left for future work.

Halo detection via large-scale Bayesian inference

We present a proof-of-concept of a novel and fully Bayesian methodology designed to detect halos of different masses in cosmological observations subject to noise and systematic uncertainties. Our methodology combines the previously published Bayesian large-scale structure inference algorithm, HADES, and a Bayesian chain rule (the Blackwell-Rao Estimator), which we use to connect the inferred density field to the properties of dark matter halos. To demonstrate the capability of our approach we construct a realistic galaxy mock catalogue emulating the wide-area 6-degree Field Galaxy Survey, which has a median redshift of approximately 0.05. Application of HADES to the catalogue provides us with accurately inferred three-dimensional density fields and corresponding quantification of uncertainties inherent to any cosmological observation. We then use a cosmological simulation to relate the amplitude of the density field to the probability of detecting a halo with mass above a specified threshold. With this information we can sum over the HADES density field realisations to construct maps of detection probabilities and demonstrate the validity of this approach within our mock scenario. We find that the probability of successful of detection of halos in the mock catalogue increases as a function of the signal-to-noise of the local galaxy observations. Our proposed methodology can easily be extended to account for more complex scientific questions and is a promising novel tool to analyse the cosmic large-scale structure in observations.

Probing the nature of dark energy

The cause for the observed acceleration in the expansion of the Universe is unknown, and referred to as “dark energy” for convenience. Dark energy could be an unknown energy component, or a modification of Einstein’s general relativity. This dictates the measurements that are optimal in unveiling the nature of dark energy: the cosmic expansion history, and the growth history of cosmic large scale structure. Type Ia supernovae, galaxy clustering, and weak lensing are generally considered the most powerful observational probes of dark energy. I will examine Type Ia supernovae and galaxy clustering as dark energy probes, and discuss the recent results and future prospects.

Consistent modified gravity analysis of anisotropic galaxy clustering using BOSS DR11

We analyse the clustering of cosmic large scale structure using a consistent modified gravity perturbation theory, accounting for anisotropic effects along and transverse to the line of sight. The growth factor has a particular scale dependence in f(R) gravity and we fit for the shape parameter f_{R0} simultaneously with the distance and the large scale (general relativity) limit of the growth function. Using more than 690,000 galaxies in the Baryon Oscillation Spectroscopy Survey Data Release 11, we find no evidence for extra scale dependence, with the 95\% confidence upper limit |f_{R0}| <8 \times 10^{-4}. Future clustering data, such as from the Dark Energy Spectroscopic Instrument, can use this consistent methodology to impose tighter constraints.

(Loop) quantum gravity and the inflationary scenario

Quantum gravity, as a fundamental theory of space-time, is expected to reveal how the universe may have started, perhaps during or before an inflationary epoch. It may then leave a potentially observable (but probably minuscule) trace in cosmic large-scale structures that seem to match well with predictions of inflation models. A systematic quest to derive such tiny effects using one approach, loop quantum gravity, has, however, led to unexpected obstacles. Such models remain incomplete, and it is not clear whether loop quantum gravity can be consistent as a full theory. But some surprising effects appear to be generic and would drastically alter our understanding of space-time at large density. These new high-curvature phenomena are a consequence of a widening gap between quantum gravity and ordinary quantum-field theory on a background.

HACC: Simulating sky surveys on state-of-the-art supercomputing architectures

Current and future surveys of large-scale cosmic structure are associated with a massive and complex datastream to study, characterize, and ultimately understand the physics behind the two major components of the ‘Dark Universe’, dark energy and dark matter. In addition, the surveys also probe primordial perturbations and carry out fundamental measurements, such as determining the sum of neutrino masses. Large-scale simulations of structure formation in the Universe play a critical role in the interpretation of the data and extraction of the physics of interest. Just as survey instruments continue to grow in size and complexity, so do the supercomputers that enable these simulations. Here we report on HACC (Hardware/Hybrid Accelerated Cosmology Code), a recently developed and evolving cosmology N-body code framework, designed to run efficiently on diverse computing architectures and to scale to millions of cores and beyond. HACC can run on all current supercomputer architectures and supports a variety of programming models and algorithms. It has been demonstrated at scale on Cell- and GPU-accelerated systems, standard multi-core node clusters, and Blue Gene systems. HACC’s design allows for ease of portability, and at the same time, high levels of sustained performance on the fastest supercomputers available. We present a description of the design philosophy of HACC, the underlying algorithms and code structure, and outline implementation details for several specific architectures. We show selected accuracy and performance results from some of the largest high resolution cosmological simulations so far performed, including benchmarks evolving more than 3.6 trillion particles.

Modern Gravitational Lens Cosmology for Introductory Physics and Astronomy Students

Recent and exciting discoveries in astronomy and cosmology have inspired many high school students to learn about these fields. A particularly fascinating consequence of general relativity at the forefront of modern cosmology research is gravitational lensing, the bending of light rays that pass near massive objects. Gravitational lensing enables high-precision mapping of dark matter distributions in galaxies and galaxy clusters, provides insight into large-scale cosmic structure of the universe, aids in the search for exo-planets, and may offer valuable insight toward understanding the evolution of dark energy. In this article we describe a gravitational lensing lab and associated lecture/discussion material that was highly successful, according to student feedback. The gravitational lens unit was developed as part of a two-week summer enrichment class for junior and senior high school students. With minor modifications, this lab can be used within a traditional classroom looking to incorporate topics of modern physics (such as in a unit on optics).

A graph of dark energy significance on different spatial and mass scales

The current cosmological paradigm sees the formation and evolution of the cosmic large-scale structure as governed by the gravitational attraction of the Dark Matter (DM) and the repulsion of the Dark Energy (DE). We characterize the relative importance of uniform and constant dark energy, as given by the Lambda term in the standard LCDM cosmology, in galaxy systems of different scales, from groups to superclusters. An instructive "Lambda significance graph" is introduced where the matter-DE density ratio <rho_M>/rho_Lambda for different galaxy systems is plotted against the radius R. This presents gravitation and DE dominated regions and shows directly the zero velocity radius, the zero-gravity radius, and the Einstein-Straus radius for any fixed value of mass. Example galaxy groups and clusters from the local universe illustrate the use of the Lambda significance graph. These are generally located deep in the gravity-dominated region <rho_M}>/rho_Lambda > 2, being virialized. Extended clusters and main bodies of superclusters can reach down near the border line between gravity-dominated and DE dominated regions <rho_M>/rho_Lambda = 2. The scale--mass relation from the standard 2-point correlation function intersects this balance line near the correlation lenght. The log <rho_M>/rho_Lambda vs. log R diagram is a useful and versatile way to characterize the dynamical state of systems of galaxies within the Lambda dominated expanding universe.

Neglecting primordial non-Gaussianity threatens future cosmological experiment accuracy

Future galaxy redshift surveys aim at probing the clustering of the cosmic large-scale structure with unprecedented accuracy, thus complementing cosmic microwave background experiments in the quest to deliver the most precise and accurate picture ever of our Universe. Analyses of such measurements are usually performed within the context of the so-called vanilla LCDM model - the six-parameter phenomenological model which, for instance, emerges from best fits against the recent data obtained by the Planck satellite. Here, we show that such an approach is prone to subtle systematics when the Gaussianity of primordial fluctuations is concerned. In particular, we demonstrate that, if we neglect even a tiny amount of primordial non-Gaussianity - fully consistent with current limits - we shall introduce spurious biases in the reconstruction of cosmological parameters. This is a serious issue that must be properly accounted for in view of accurate (as well as precise) cosmology.

Past and present cosmic structure in the SDSS DR7 main sample

We present a chrono-cosmography project, aiming at the inference of the four dimensional formation history of the observed large scale structure from its origin to the present epoch. To do so, we perform a full-scale Bayesian analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS) Data Release 7 main galaxy sample, relying on a fully probabilistic, physical model of the non-linearly evolved density field. Besides inferring initial conditions from observations, our methodology naturally and accurately reconstructs non-linear features at the present epoch, such as walls and filaments, corresponding to high-order correlation functions generated by late-time structure formation. Our inference framework self-consistently accounts for typical observational systematic and statistical uncertainties such as noise, survey geometry and selection effects. We further account for luminosity dependent galaxy biases and automatic noise calibration within a fully Bayesian approach. As a result, this analysis provides highly-detailed and accurate reconstructions of the present density field on scales larger than ∼ 3 Mpc/h, constrained by SDSS observations. This approach also leads to the first quantitative inference of plausible formation histories of the dynamic large scale structure underlying the observed galaxy distribution. The results described in this work constitute the first full Bayesian non-linear analysis of the cosmic large scale structure with the demonstrated capability of uncertainty quantification. Some of these results will be made publicly available along with this work. The level of detail of inferred results and the high degree of control on observational uncertainties pave the path towards high precision chrono-cosmography, the subject of simultaneously studying the dynamics and the morphology of the inhomogeneous Universe.

Matrix-free large-scale Bayesian inference in cosmology

In this work we propose a new matrix-free implementation of the Wiener sampler which is traditionally applied to high dimensional analysis when signal covariances are unknown. Specifically, the proposed method addresses the problem of jointly inferring a high dimensional signal and its corresponding covariance matrix from a set of observations. Our method implements a Gibbs sampling adaptation of the previously presented messenger approach, permitting to cast the complex multivariate inference problem into a sequence of uni-variate random processes. In this fashion, the traditional requirement of inverting high dimensional matrices is completely eliminated from the inference process, resulting in an efficient algorithm that is trivial to implement. Using cosmic large scale structure data as a showcase, we demonstrate the capabilities of our Gibbs sampling approach by performing a joint analysis of three dimensional density fields and corresponding power-spectra from Gaussian mock catalogues. These tests clearly demonstrate the ability of the algorithm to accurately provide measurements of the three dimensional density field and its power-spectrum and corresponding uncertainty quantification. Moreover, these tests reveal excellent numerical and statistical efficiency which will generally render the proposed algorithm a valuable addition to the toolbox of large scale Bayesian inference in cosmology and astrophysics.