Testing gaussianity, homogeneity and isotropy with the cosmic microwave background
L. Raul Abramo, Thiago S. Pereira
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52 pages, 22 pdf figures. Revised version of the invited review for the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" for Advances in Astronomy.
We review the basic hypotheses which motivate the statistical framework used to analyze the cosmic microwave background, and how that framework can be enlarged as we relax those hypotheses. In particular, we try to separate as much as possible the questions of gaussianity, homogeneity and isotropy from each other. We focus both on isotropic estimators of non-gaussianity as well as statistically anisotropic estimators of gaussianity, giving particular emphasis on their signatures and the enhanced "cosmic variances" that become increasingly important as our putative Universe becomes less symmetric. After reviewing the formalism behind some simple model-independent tests, we discuss how these tests can be applied to CMB data when searching for large scale "anomalies"
Using the 2MASS Photometric Redshift catalogue we perform a number of statistical tests aimed at detecting possible departures from statistical homogeneity and isotropy in the large-scale structure of the Universe. Making use of the angular homogeneity index, an observable proposed in a previous publication, as well as studying the scaling of the angular clustering and number counts with magnitude limit, we place constraints on the fractal nature of the galaxy distribution. We find that the statistical properties of our sample are in excellent agreement with the standard cosmological model, an…
We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are elementary and well-known, namely Einstein's theory of gravity and Hawking's method of computing gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for "big bang" type singularities dominated by conformal matter, enforcing $CPT$ symmetry and analyticity. Here, we show that, besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons, enabling us to calculate the gravit…
The last few years have seen a surge in excitement about measurements of statistics of the primordial fluctuations beyond the power spectrum. New ideas for precision tests of Gaussianity and statistical isotropy in the data are developing simultaneously with proposals for a wide range of new theoretical possibilities. From both the observations and theory, it has become clear that there is a huge discovery potential from upcoming measurements. In this Special Issue of Advances in Astronomy we have collected articles that summarize the theoretical predictions for departures from Gaussianity or …
A 2.29 GHz VLBI all-sky survey of ultra-compact radio sources has formed the basis of a number of cosmological investigations, which examine the relationship between angular-size and redshift. Here I use a sample of 468 such sources with 0.5<z<=3.787, to investigate the isotropy of the Universe. The sample is divided into hemispherical sub-samples, over an all-sky 5 degree x 5 degree array, each of which is allowed to determine a value of Omega_m, assuming that we are living in a spatially flat homogeneous isotropic LambdaCDM model. If we regard the latter as a null hypothesis, then it fails t…
Despite its fundamental importance in cosmology, there have been very few straight-forward tests of the cosmological principle. Such tests are especially timely because of the hemispherical asymmetry in the cosmic microwave background recently observed by the Planck collaboration. Most tests to date looked at the redshift dependence of cosmological parameters. These are subject to large systematic effects that require modeling and bias corrections. Unlike previous tests, the tests described here compare galaxy distributions in equal volumes at the same redshift z. This allows a straight-forwar…
Accurate component separation of full-sky maps in the radio and microwave frequencies, such as the cosmic microwave background (CMB), relies on a thorough understanding of the statistical properties of the Galactic foreground emissions. Using scalar Minkowski functionals and their tensorial generalization known as Minkowski tensors, we analyze the statistical properties of one of the major foreground components, namely the Galactic synchrotron given by the full sky 408 MHz Haslam map. We focus on understanding the nature of non-Gaussianity and statistical isotropy of the cooler regions of the …
Most inflationary models predict primordial perturbations to be statistically isotropic and homogeneous. Cosmic microwave background (CMB) observations, however, indicate a possible departure from statistical isotropy in the form of a dipolar power modulation at large angular scales. Alternative models of inflation, beyond the simplest single-field slow-roll models, can generate a small power asymmetry, consistent with these observations. Observations of clustering of quasars show, however, agreement with statistical isotropy at much smaller angular scales. Here, we propose to use off-diagonal…
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of purported isotropic Gaussian random fields on the sphere. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the {\it Planck} collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. To study the randomness of the fields represented by each map we use the autocorrelation of the sequence of probe coefficients (which are just the full-sky Fourier coefficients $a_{\ell,0}$ if the $z$ axis is taken in the probe direction).…
We propose a method to probe the homogeneity of a general universe, without assuming symmetry. We show that isotropy can be tested at remote locations on the past lightcone by comparing the line-of-sight and transverse expansion rates, using the time dependence of the polarization of Cosmic Microwave Background photons that have been inverse-Compton scattered by the hot gas in massive clusters of galaxies. This probes a combination of remote transverse and parallel components of the expansion rate of the metric, and we may use radial baryon acoustic oscillations or cosmic clocks to measure the…
Isotropy, anisotropies and non-Gaussianity in the scalar-induced gravitational-wave background: diagrammatic approach for primordial non-Gaussianity up to arbitrary order
Hangzhou Normal University（杭州师范大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；National Astronomical Observatory of Japan（日本国立天文台）；SOKENDAI（综合研究大学院大学）；China Agricultural University（中国农业大学）；KEK（高能加速器研究机构）；The University of Tokyo（东京大学）
The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the CMB and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past lightcone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity, we need to assume the Copern…
We present the first measurement of the homogeneity index, $\mathcal{H}$, a fractal or Hausdorff dimension of the early Universe from the Planck CMB temperature variations $δT$ in the sky. This characterization of the isotropy scale is model-free and purely geometrical, independent of the amplitude of $δT$. We find evidence of homogeneity ($\mathcal{H}=0$) for scales larger than $θ_{\mathcal{H}} = 65.9 \pm 9.2 °$ on the CMB sky. This finding is at odds with the $Λ$CDM prediction, which assumes a scale invariant infinite universe. Such anomaly is consistent with the well known low quadrupule am…
The BOSS quasar sample is used to study cosmic homogeneity with a 3D survey in the redshift range $2.2<z<2.8$. We measure the count-in-sphere, $N(<\! r)$, i.e. the average number of objects around a given object, and its logarithmic derivative, the fractal correlation dimension, $D_2(r)$. For a homogeneous distribution $N(<\! r) \propto r^3$ and $D_2(r)=3$. Due to the uncertainty on tracer density evolution, 3D surveys can only probe homogeneity up to a redshift dependence, i.e. they probe so-called "spatial isotropy". Our data demonstrate spatial isotropy of the quasar distribution in the red…
The assumption of homogeneity and isotropy on large scales is one of the main hypotheses of the standard cosmology. In this paper, we test the hypothesis of isotropy from the two-point angular correlation function of 2626 gamma-ray bursts (GRB) of the FERMI GRB catalogue. We show that the uncertainties in the GRB positions induce spurious anisotropic signals in their sky distribution. However, when such uncertainties are taken into account no significant evidence against the large-scale statistical isotropy is found. This result remains valid even for the sky distribution of short-lived GRB, c…
The assumption of homogeneity and isotropy on large scales is one of the main hypotheses of the standard cosmological model. In this paper, we revisit a test of cosmological isotropy using type Ia supernova (SN Ia) distances provided by the latest SN Ia compilation available, namely, the Pantheon compilation. We perform a model-independent analysis by selecting low-redshift subsamples lying in two redshift intervals, i.e., z $\leq$ 0.10 and z $\leq$ 0.20. By mapping the directional asymmetry of cosmological parameters across the sky, we show that the current SN Ia data favor the hypothesis of …
We derive a general expression for the probability of observing deviations from statistical isotropy in the cosmic microwave background (CMB) if the primordial fluctuations are non-Gaussian and extend to superhorizon scales. The primary motivation is to properly characterize the monopole and dipole modulations of the primordial power spectrum that are generated by the coupling between superhorizon and subhorizon perturbations. Unlike previous proposals for generating the hemispherical power asymmetry, we do not assume that the power asymmetry results from a single large superhorizon mode. Inst…
Quantum Signatures of Cosmic Topology: How Casimir Backreaction Transmits Isotropy Violation
Case Western Reserve University（凯斯西储大学）；Instituto de Física Teórica (IFT) UAM-CSIC（马德里自治大学-西班牙国家科学研究委员会理论物理研究所）；Imperial College London（帝国理工学院）；INFN, Sezione di Padova（意大利国家核物理学院帕多瓦分部）；Università degli Studi di Padova（帕多瓦大学）；Laboratoire Univers et Théories, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS（巴黎天文台宇宙与理论实验室（巴黎文理研究大学、巴黎西岱大学、法国国家科学研究中心））
In this work we study the imprints of a primordial cosmic string on inflationary power spectrum. Cosmic string induces two distinct contributions on curvature perturbations power spectrum. The first type of correction respects the translation invariance while violating isotropy. This generates quadrupolar statistical anisotropy in CMB maps which is constrained by the Planck data. The second contribution breaks both homogeneity and isotropy, generating a dipolar power asymmetry in variance of temperature fluctuations with its amplitude falling on small scales. We show that the strongest constra…
Testing the cosmological principle on gigaparsec scales
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-Hongkong-Macau Greater Bay Area,Sun Yat-sen University（中山大学粤港澳大湾区空间站科学中心）
Cosmic Microwave Background (CMB) Anisotropies is a subject of intensive research in several fields of sciences. In this paper we start a systematic development of basic notions and theory in statistics according to the application for CMB. The main result of this paper is the necessary and sufficient condition for isotropy of a non-Gaussian field in terms of spectra. Clear formulae for bi-, tri- and polyspectra and bi-, tri-, and higher order covariances are also given. Keywords: Bispectrum, Trispectrum, Angular poly-Spectra, Cosmic microwave background radiation; Gaussianity; spherical rando…
In this article we propose a novel test for statistical anisotropy of the CMB. The test is based on the fact, that the Galactic foregrounds have a remarcably strong symmetry with respect to their antipodal points and with respect to the Galactic plane, while the cosmological signal should not be symmetric or asymmetric under these transitions. We have applied the test for the octupole component of the WMAP ILC 7 map, by looking at a_3,1 and a_3,3, and their ratio to a_3,2 both for real and imaginary values. We find abnormal symmetry of the octupole component at the level of 0.58%, compared to …
A central assumption in our analysis of cosmic structure is that cosmological perturbations have zero ensemble mean. This property is one of the consequences of statistically homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which perturbations have non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, …
The measurement of the inflationary stochastic gravitational-wave background (SGWB) is one of the main goals of future GW experiments. In direct GW experiments, an obstacle to achieving it is the isolation of the inflationary SGWB from the other types of SGWB. In this paper, as a distinguishable signature of the inflationary SGWB, we argue the detectability of its universal property: antipodal correlations, i.e., correlations of GWs from the opposite directions, as a consequence of the horizon re-entry. A phase-coherent method has been known to be of no use for detecting the angular correlatio…
