Toward a Complete Cosmological Analysis of Galaxy Clustering Measurements from Spectroscopic Redshift Surveys

The forthcoming generation of galaxy redshift surveys will sample the large-scale structure of the Universe over unprecedented volumes with high-density tracers. This advancement will make robust measurements of three-point clustering statistics not only possible, but necessary in order to exploit the surveys full potential to constrain cosmological models. My Ph.D. project is conceived specically for this improvement. Its main goal is the development of a software pipeline for the analysis of the joined galaxy power spectrum and bispectrum. In a rst stage, my collaborators and I investigate how several methodological choices can inuence inferences based on the bispectrum about galaxy bias and shot noise. We consider dark-matter halos, extracted from N-body simulations, of at least 1013Mb. While these are not representative of a realistic distribution of objects that is observed by redshift surveys, it is possible to extract a large number of synthetic catalogs of this type of objects from N-body simulations, and this still allows for comparison of perturbative models. We estimate the covariance matrix of the measurement errors by using 10,000 mock catalogues generated with the Pinocchio code, and then we t a series of theoretical models based on tree-level perturbation theory to the numerical data. We study how the model constraints are in uenced by the binning strategy for the bispectrum congurations and by the form of the likelihood function. We also use Bayesian model-selection techniques to single out the optimal theoretical description of our data. We nd that a three-parameter bias model at treelevel combined with Poissonian shot noise is necessary to model the halo bispectrum up to scales of kmax f 0:09 hMpc 121, although tting formulae that relate the bias parameters can be helpful to reduce the freedom of the model without compromising accuracy. Our data clearly disfavour local Eulerian and local Lagrangian bias models and do not require corrections to Poissonian shot noise. We then approach our nal goal of a simultaneous analysis of the power spectrum and bispectrum in real space. We t measurements of power spectrum and bispectrum of dark-matter halos from the same set of N-body simulations, with a full covariance, including cross correlations between power spectrum and bispectrum, estimated by the same 10,000 mock catalogues. The theoretical models employed are perturbative predictions at tree-level for the bispectrum, and at one-loop level for the power spectrum, both based on the Eective Field Theory of the Large Scale Structure, including infrared resummation, that represent the state of the art in the analysis of galaxy clustering measurements. We focus on the constraints of bias and shot-noise parameters as a function of kmax, we study extensions of the parameter space and possible reductions through either phenomenological of physically-motivated bias relations; we explore the impact of dierent covariance approximations and binning eects on the theoretical predictions. We nd that a joint t of power spectrum and bispectrum with 4 bias parameters, one EFT counterterm and two shot-noise parameters gives a good description of our data up to kmax;P 0:21 hMpc 121 and kmax;B 0:09 hMpc 121. In this particular setup, we perform a simultaneous t of power spectrum and bispectrum including cosmological parameters, and consistently evaluating the theoretical predictions at each sampled point in parameter space. We recover the correct value of the cosmological parameters used to run the N-body simulations. We envision that the addition of the galaxy bispectrum to the galaxy power spectrum, being able to break degeneracies between the model parameters, will allow much tighter constraints on cosmological parameters in future analyses of actual data

Advancing the Matter Bispectrum Estimation in Large-Scale Structure

The $\Lambda$CDM model for the Universe is highly successful in explaining cosmological observations to date, and its parameters tightly constrained by Cosmic Microwave Background (CMB) experiments such as Planck. Higher-order statistics, like the three-point correlation function or bispectrum in Fourier space, will be indispensable for furthering our understanding of the Universe. While these methodologies have been developed over the years and applied to CMB analyses, similar work on large-scale structure is still in its infancy. Additionally, information from future galaxy surveys such as LSST and Euclid will soon exceed that available from the CMB, demonstrating a pressing need for such tools. The theoretical modelling of non-linear gravitational interactions is difficult beyond the perturbative regime, necessitating large, expensive $N$-body dark matter simulations to understand the small-scale dynamics. Additionally, the direct numerical computation of the matter bispectrum is intractable due to the multiplicity of triangular configurations. In this Thesis, we make breakthroughs in both of these problems. First, we present the newly rewritten MODAL-LSS formalism that enables efficient and optimal estimation of the full bispectrum for any matter density field to unprecedented accuracy, as well as demonstrating rapid convergence which makes it ideal for the analysis of large datasets. This has allowed us to benchmark fast dark matter codes (e.g. particle-mesh or L-PICOLA) against GADGET-3 using the bispectrum, showing quantitatively how the mismatch at large $k$ can be improved with a simple boosting technique in the power spectrum. We have also estimated the non-Gaussian contribution to the dark matter bispectrum covariance, which cannot be computed analytically in the non-linear regime. This will be vital for the extraction of cosmological parameters from data in the future. In preparation for the analysis of future galaxy datasets we have also investigated the non-trivial problem of linking the underlying dark matter density field to the observed galaxy distribution. As an important milestone we have investigated the effects of the halo profile, the Halo Occupation Distribution (HOD) model, and multivariate assembly bias models of the halo occupation and concentration on the power spectrum and full bispectrum of a subhalo catalogue derived from the ROCKSTAR halo finder. These fast, phenomenological methods allow us to pave the way for the efficient generation of mock galaxy catalogues.My PhD was generously funded by the Cambridge Commonwealth, European and International Trust and the Croucher Foundation. I have additionally received invaluable financial assistance from St. Catharine's College, Cambridge, the Cambridge Philosophical Society, the Department of Applied Mathematics and Theoretical Physics, and the Centre for Theoretical Cosmology in my final year

Bayesian large-scale structure inference and cosmic web analysis

Surveys of the cosmic large-scale structure carry opportunities for building and testing cosmological theories about the origin and evolution of the Universe. This endeavor requires appropriate data assimilation tools, for establishing the contact between survey catalogs and models of structure formation. In this thesis, we present an innovative statistical approach for the ab initio simultaneous analysis of the formation history and morphology of the cosmic web: the BORG algorithm infers the primordial density fluctuations and produces physical reconstructions of the dark matter distribution that underlies observed galaxies, by assimilating the survey data into a cosmological structure formation model. The method, based on Bayesian probability theory, provides accurate means of uncertainty quantification. We demonstrate the application of BORG to the Sloan Digital Sky Survey data and describe the primordial and late-time large-scale structure in the observed volume. We show how the approach has led to the first quantitative inference of the cosmological initial conditions and of the formation history of the observed structures. We then use these results for several cosmographic projects aiming at analyzing and classifying the large-scale structure. In particular, we build an enhanced catalog of cosmic voids probed at the level of the dark matter distribution, deeper than with the galaxies. We present detailed probabilistic maps of the dynamic cosmic web, and offer a general solution to the problem of classifying structures in the presence of uncertainty. The results described in this thesis constitute accurate chrono-cosmography of the inhomogeneous cosmic structure.Comment: 237 pages, 63 figures, 14 tables. PhD thesis, Institut d'Astrophysique de Paris, September 2015 (advisor: B. Wandelt). Contains the papers arXiv:1305.4642, arXiv:1409.6308, arXiv:1410.0355, arXiv:1502.02690, arXiv:1503.00730, arXiv:1507.08664 and draws from arXiv:1403.1260. Full version including high-resolution figures available from the author's websit

Large-Scale Galaxy Bias

This review presents a comprehensive overview of galaxy bias, that is, the statistical relation between the distribution of galaxies and matter. We focus on large scales where cosmic density fields are quasi-linear. On these scales, the clustering of galaxies can be described by a perturbative bias expansion, and the complicated physics of galaxy formation is absorbed by a finite set of coefficients of the expansion, called bias parameters. The review begins with a detailed derivation of this very important result, which forms the basis of the rigorous perturbative description of galaxy clustering, under the assumptions of General Relativity and Gaussian, adiabatic initial conditions. Key components of the bias expansion are all leading local gravitational observables, which include the matter density but also tidal fields and their time derivatives. We hence expand the definition of local bias to encompass all these contributions. This derivation is followed by a presentation of the peak-background split in its general form, which elucidates the physical meaning of the bias parameters, and a detailed description of the connection between bias parameters and galaxy statistics. We then review the excursion-set formalism and peak theory which provide predictions for the values of the bias parameters. In the remainder of the review, we consider the generalizations of galaxy bias required in the presence of various types of cosmological physics that go beyond pressureless matter with adiabatic, Gaussian initial conditions: primordial non-Gaussianity, massive neutrinos, baryon-CDM isocurvature perturbations, dark energy, and modified gravity. Finally, we discuss how the description of galaxy bias in the galaxies' rest frame is related to clustering statistics measured from the observed angular positions and redshifts in actual galaxy catalogs.Comment: 259 pages, 39 figures, 15 tables; published in Physics Reports; v2: minor corrections and clarifications, references added; v3: substantially revised and improved version; v4: minor edits and clarifications reflecting published version, corrected mistakes in Eqs. (7.57)-(7.58); v5: minor corrections [Eq. (5.5)] and updated reference

Accelerating inference in cosmology and seismology with generative models

Statistical analyses in many physical sciences require running simulations of the system that is being examined. Such simulations provide complementary information to the theoretical analytic models, and represent an invaluable tool to investigate the dynamics of complex systems. However, running simulations is often computationally expensive, and the high number of required mocks to obtain sufficient statistical precision often makes the problem intractable. In recent years, machine learning has emerged as a possible solution to speed up the generation of scientific simulations. Machine learning generative models usually rely on iteratively feeding some true simulations to the algorithm, until it learns the important common features and is capable of producing accurate simulations in a fraction of the time. In this thesis, advanced machine learning algorithms are explored and applied to the challenge of accelerating physical simulations. Various techniques are applied to problems in cosmology and seismology, showing benefits and limitations of such an approach through a critical analysis. The algorithms are applied to compelling problems in the fields, including surrogate models for the seismic wave equation, the emulation of cosmological summary statistics, and the fast generation of large simulations of the Universe. These problems are formulated within a relevant statistical framework, and tied to real data analysis pipelines. In the conclusions, a critical overview of the results is provided, together with an outlook over possible future expansions of the work presented in the thesis

Statistical properties of cosmological correlation functions

Correlation functions are an omnipresent tool in astrophysics, and they are routinely used to study phenomena as diverse as the large-scale structure of the Universe, time-dependent pulsar signals, and the cosmic microwave background. In many cases, measured correlation functions are analyzed in the framework of Bayesian statistics, which requires knowledge about the likelihood of the data. In the case of correlation functions, this probability distribution is usually approximated as a multivariate Gaussian, which is not necessarily good approximation -- hence, this work aims at finding a better description. To this end, we exploit fundamental mathematical constraints on correlation functions, which we use to construct a quasi-Gaussian likelihood. We explain how to compute the constraints, in particular for multi-dimensional random fields, where this can only be done numerically, check the quality of the quasi-Gaussian approximation, and compare it to alternative approaches -- most importantly, we test the new-found description of the likelihood in a toy-model Bayesian analysis. Finally, we compute correlation functions from the Millennium Simulation and show that they obey the constraints. By studying statistical properties of the measured correlation functions, we present further indications for the validity of the quasi-Gaussian approach

The non-Gaussian matter power spectrum covariance in the halo model approach

Weak gravitational lensing is one of the most promising tools to analyze the nature of dark energy and dark matter. In order to constrain cosmological parameters with this method a good theoretical understanding of the underlying dark matter density field is necessary. This work provides an analytical treatment of higher-order correlation functions in the dark matter density field and compares the results obtained with numerical N-body simulations. The tool of choice is a semi-analytic halo model which combines results from perturbation theory and N-body simulations. The main emphasis of this work is on the fourth-order correlation function and its Fourier counterpart, the trispectrum, since it allows us to study the non-Gaussianities of the dark matter field and to calculate the full non-Gaussian covariance of the power spectrum. This provides a way to estimate the error and mode coupling in the dark matter power spectrum to higher accuracy than has been previously. After deriving an analytical expression for the expectation value of the three-dimensional and the convergence power spectrum covariance, we use the halo model to make explicit predictions for different cosmological models. Additionally, we analyze the impact of a stochastic concentration parameter on the non-Gaussian contribution to the power spectrum covariance. To minimize the computational effort to calculate the full non-Gaussian covariance, different approximations are studied within the halo model approach, and a fitting formula is derived that allows instant calculation of the convergence power spectrum covariance over a wide range of cosmological parameters.</p

Observational Probes of Cosmic Acceleration

The accelerating expansion of the universe is the most surprising cosmological discovery in many decades, implying that the universe is dominated by some form of "dark energy" with exotic physical properties, or that Einstein's theory of gravity breaks down on cosmological scales. The profound implications of cosmic acceleration have inspired ambitious experimental efforts to measure the history of expansion and growth of structure with percent-level precision or higher. We review in detail the four most well established methods for making such measurements: Type Ia supernovae, baryon acoustic oscillations (BAO), weak gravitational lensing, and galaxy clusters. We pay particular attention to the systematic uncertainties in these techniques and to strategies for controlling them at the level needed to exploit "Stage IV" dark energy facilities such as BigBOSS, LSST, Euclid, and WFIRST. We briefly review a number of other approaches including redshift-space distortions, the Alcock-Paczynski test, and direct measurements of H_0. We present extensive forecasts for constraints on the dark energy equation of state and parameterized deviations from GR, achievable with Stage III and Stage IV experimental programs that incorporate supernovae, BAO, weak lensing, and CMB data. We also show the level of precision required for other methods to provide constraints competitive with those of these fiducial programs. We emphasize the value of a balanced program that employs several of the most powerful methods in combination, both to cross-check systematic uncertainties and to take advantage of complementary information. Surveys to probe cosmic acceleration produce data sets with broad applications, and they continue the longstanding astronomical tradition of mapping the universe in ever greater detail over ever larger scales.Comment: 289 pages, 55 figures. Accepted for publication in Physics Reports. Description of changes since original version --- fractionally small but significant in total --- is available at http://www.astronomy.ohio-state.edu/~dhw/Revie

Cosmic Shear and the Intrinsic Alignment of Galaxies

Cosmology has recently entered an era of increasingly rich observational data sets, all being in agreement with a cosmological standard model that features only a small number of free parameters. One of the most powerful techniques to constrain these parameters and test the accuracy of the concordance model is the weak gravitational lensing of distant galaxies by the large-scale structure, or cosmic shear. This thesis investigates the optimisation of present and future cosmic shear surveys with respect to the extraction of cosmological information and deals with the characterisation and control of the intrinsic alignment of galaxies, a major systematic in cosmic shear data. A detailed derivation of the covariance of the weak lensing convergence bispectrum is presented, clarifying the relation between existing formalisms, providing illustration, and simplifying the practical computation. The results are then applied to forecasts on cosmological constraints by cosmic shear two- and three-point statistics with the proposed Euclid satellite. Besides, a novel method to assess the impact of unknown systematics on cosmological parameter constraints is summarised, and several aspects concerning the weak lensing analysis of the Hubble Space Telescope COSMOS survey are highlighted. A synopsis of the current state of knowledge about the intrinsic alignment of galaxies is given, including its physical origin, modelling attempts, simulation results, and existing observations. Possible corrections to the prevailing model of intrinsic alignments are suggested, before presenting new observational constraints on matter-intrinsic shear correlations using several galaxy samples from the Sloan Digital Sky Survey. For the first time a data set with only photometric redshift information is included, after developing the formalism for correlation function models that take photometric redshift scatter into account. The intrinsic alignment signal of early-type galaxies is found to increase with galaxy luminosity and to be inconsistent with the default redshift evolution of a widely used model, both with high confidence. Moreover the nulling technique is developed, a method to remove gravitational shear-intrinsic ellipticity correlations from cosmic shear data by solely relying on the well-known redshift dependence of the signals, and its performance on realistically modelled cosmic shear two-point statistics is investigated. Subsequently, the principle of intrinsic alignment boosting, an inverse and likewise geometrical approach capable of extracting the intrinsic alignment signal from cosmic shear data, is derived. Both techniques are shown to robustly remove or isolate the intrinsic alignment signal, but are subject to a significant loss of statistical power caused by the similarity between the redshift dependence of the lensing signal and shear-intrinsic correlations in combination with strict model independence. As an alternative ansatz, the joint analysis of various probes available from cosmic shear surveys is considered, including cosmic shear, galaxy clustering, lensing magnification effects, and cross-correlations between galaxy number densities and shapes. The self-calibration capabilities of intrinsic alignments and the galaxy bias in the combined data are found to be excellent for realistic survey parameters, recovering the constraints on cosmological parameters for a pure cosmic shear signal in presence of flexible parametrisations of intrinsic alignments and galaxy bias with about a hundred nuisance parameters in total

Approach for Improved Signal-Based Fault Diagnosis of Hot Rolling Mills

Der hier vorgestellte Ansatz ist in der Lage, zwei spezifische schwere Fehler zu erkennen, sie zu identifizieren, zwischen vier verschiedenen Systemzuständen zu unterscheiden und eine Prognose bezüglich des Systemverhaltens zu geben. Die vorliegende Arbeit untersucht die Zustandsüberwachung des komplexen Herstellungsprozesses eines Warmbandwalzwerks. Eine signalbasierte Fehlerdiagnose und ein Fehlerprognoseansatz für den Bandlauf werden entwickelt. Eine Literaturübersicht gibt einen Überblick über die bisherige Forschung zu verwandten Themen. Es wird gezeigt, dass die große Anzahl vorheriger Arbeiten diese Thematik nicht gelöst hat und dass weitere Untersuchungen erforderlich sind, um eine zufriedenstellende Lösung der behandelten Probleme zu erhalten. Die Entwicklung einer neuen Signalverarbeitungskette und die Signalverarbeitungsschritte sind detailliert dargestellt. Die Klassifikationsaufgabe wird in Fehlerdiagnose, Fehleridentifikation und Fehlerprognose differenziert. Der vorgeschlagene Ansatz kombiniert fünf verschiedene Methoden zur Merkmalsextraktion, nämlich Short-Time Fourier Transformation, kontinuierliche Wavelet Transformation, diskrete Wavelet Transformation, Wigner-Ville Distribution und Empirical Mode Decomposition, mit zwei verschiedenen Klassifikationsalgorithmen, nämlich Support-Vektor Maschine und eine Variation der Kreuzkorrelation, wobei letztere in dieser Arbeit entwickelt wurde. Kombinationen dieser Merkmalsextraktion und Klassifikationsverfahren werden an Walzkraft-Daten aus einer Warmbreitbandstraße angewendet.The approach introduced here is able to detect two specific severe faults, to identify them, to distinguish between four different system states, and to give a prognosis on the system behavior. The presented work investigates the condition monitoring of the complex production process of a hot strip rolling mill. A signal-based fault diagnosis and fault prognosis approach for strip travel is developed. A literature review gives an overview about previous research on related topics. It is shown that the great amount of previous work does not cope with the problems treated in this work and that further investigation is necessary to provide a satisfactory solution. The design of a new signal processing chain is presented and the signal processing steps are detailed. The classification task is differentiated into fault detection, fault identification and fault prognosis. The proposed approach combines five different methods for feature extraction, namely short time Fourier transform, continuous wavelet transform, discrete wavelet transform, Wigner-Ville distribution, and empirical mode decomposition, with two different classification algorithms, namely support vector machine and a variation of cross-correlation, the latter developed in this work. Combinations of these feature extraction and classification methods are applied to rolling force data originating from a hot strip mill