Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski functionals

Buchert, Thomas; France, Martin J.; Steiner, Frank

doi:10.1088/1361-6382/aa5ce2

Cited by 44 publications

(48 citation statements)

References 119 publications

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“…Figure 2 shows values of the coefficients a n acquired from Planck CMB maps (see also Ref. [21] for a similar analysis). The coefficients were obtained by counting the occurrences of Θ values in Planck's SMICA temperature map.…”

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confidence: 99%

Reconstructing the Inflationary Landscape with Cosmological Data

et al. 2018

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We show that the shape of the inflationary landscape potential may be constrained by analyzing cosmological data. The quantum fluctuations of fields orthogonal to the inflationary trajectory may have probed the structure of the local landscape potential, inducing non-Gaussianity (NG) in the primordial distribution of the curvature perturbations responsible for the cosmic microwave background (CMB) anisotropies and our Universe's large-scale structure. The resulting type of NG (tomographic NG) is determined by the shape of the landscape potential, and it cannot be fully characterized by 3-or 4-point correlation functions. Here we deduce an expression for the profile of this probability distribution function in terms of the landscape potential, and we show how this can be inverted in order to reconstruct the potential with the help of CMB observations. While current observations do not allow us to infer a significant level of tomographic NG, future surveys may improve the possibility of constraining this class of primordial signatures.Is there any feature about our Universe that would require us to assume primordial non-Gaussian initial conditions? Up until now, cosmic microwave background (CMB) and large-scale structure (LSS) observations are fully consistent with the premise that the primordial curvature perturbations were initially distributed according to a perfectly Gaussian statistics [1,2]. This has favored the simplest models of inflation -single field slowroll inflation-based on the steady evolution of a scalar field driven by a flat potential [3][4][5][6][7]. In these models, the self-interactions of the primordial curvature perturbation lead to tiny non-Gaussianities suppressed by the slow-roll parameters characterizing the evolution of the Hubble expansion rate H, during inflation [8][9][10][11].The confirmation of non-Gaussian initial conditions would help us to decipher certain fundamental aspects about inflation [12][13][14][15]. Indeed, non-Gaussianity (NG) can be generated by nonlinearities affecting the evolution of primordial curvature perturbations (denoted as ζ). These nonlinearities are the result of self-interactions, or interactions with other degrees of freedom, such as isocurvature fields (fields orthogonal to the inflationary trajectory in multifield space). Inevitably, perturbation theory limits the extent to which we can study the emergence of NG, forcing us to focus on the lowest order operators (in terms of field powers) in the ζ Lagrangian. Thus, most of the recent effort devoted to the study of NG has relied on parametrizing it with the bispectrum and trispectrum, the amplitudes of the 3-and 4-point correlation functions of ζ in momentum space. Understanding how different interactions lead to different shapes and runnings of the bispectrum has constituted one of the main programs in the study of inflation [12][13][14][15].It is conceivable, however, that certain classes of interactions may lead to NG deviations that cannot be parametrized just with the bispectrum and/or trispectrum....

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confidence: 99%

Reconstructing the Inflationary Landscape with Cosmological Data

et al. 2018

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“…Both the assumptions of Gaussianity and homogeneity have been challenged recently, from both theoretical and empirical viewpoints [22,34], and is the issue of homogeneity that we wish to address now, using PDs and Gibbs models. (The issue of Gaussianity is addressed in far more detail, using topological methods, albeit different to the ones that we are using here, in [39], and with geometrical methods in [37,11]. )…”

Section: Example 2: Cmb Non-homogeneitymentioning

confidence: 99%

Modeling and replicating statistical topology and evidence for CMB nonhomogeneity

Adler

Agami

Pranav

2017

Proc. Natl. Acad. Sci. U.S.A.

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Under the banner of "big data," the detection and classification of structure in extremely large, high-dimensional, data sets are two of the central statistical challenges of our times. Among the most intriguing new approaches to this challenge is "TDA," or "topological data analysis," one of the primary aims of which is providing nonmetric, but topologically informative, preanalyses of data which make later, more quantitative, analyses feasible. While TDA rests on strong mathematical foundations from topology, in applications, it has faced challenges due to difficulties in handling issues of statistical reliability and robustness, often leading to an inability to make scientific claims with verifiable levels of statistical confidence. We propose a methodology for the parametric representation, estimation, and replication of persistence diagrams, the main diagnostic tool of TDA. The power of the methodology lies in the fact that even if only one persistence diagram is available for analysis-the typical case for big data applications-the replications permit conventional statistical hypothesis testing. The methodology is conceptually simple and computationally practical, and provides a broadly effective statistical framework for persistence diagram TDA analysis. We demonstrate the basic ideas on a toy example, and the power of the parametric approach to TDA modeling in an analysis of cosmic microwave background (CMB) nonhomogeneity.

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“…(See also [13] for a comprehensive description of the development of the subject and list of references.) These are defined on real space and contain correlations of arbitrary order.…”

Section: Introductionmentioning

confidence: 99%

Tensor Minkowski Functionals for random fields on the sphere

Chingangbam

Yogendran

Joby

et al. 2017

J. Cosmol. Astropart. Phys.

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Abstract. We generalize the translation invariant tensor-valued Minkowski Functionals which are defined on two-dimensional flat space to the unit sphere. We apply them to level sets of random fields. The contours enclosing boundaries of level sets of random fields give a spatial distribution of random smooth closed curves. We outline a method to compute the tensor-valued Minkowski Functionals numerically for any random field on the sphere. Then we obtain analytic expressions for the ensemble expectation values of the matrix elements for isotropic Gaussian and Rayleigh fields. The results hold on flat as well as any curved space with affine connection. We elucidate the way in which the matrix elements encode information about the Gaussian nature and statistical isotropy (or departure from isotropy) of the field. Finally, we apply the method to maps of the Galactic foreground emissions from the 2015 PLANCK data and demonstrate their high level of statistical anisotropy and departure from Gaussianity.

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Model-independent analyses of non-Gaussianity in Planck CMB maps using Minkowski functionals

Cited by 44 publications

References 119 publications

Reconstructing the Inflationary Landscape with Cosmological Data

Reconstructing the Inflationary Landscape with Cosmological Data

Modeling and replicating statistical topology and evidence for CMB nonhomogeneity

Tensor Minkowski Functionals for random fields on the sphere

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