We apply our symmetry based Power tensor technique to test conformity of PLANCK Polarization maps with statistical isotropy. On a wide range of angular scales (l=40-150), our preliminary analysis detects many statistically anisotropic multipoles in foreground cleaned full sky PLANCK polarization maps viz., COMMANDER and NILC. We also study the effect of residual foregrounds that may still be present in the galactic plane using both common UPB77 polarization mask, as well as the individual component separation method specific polarization masks. However some of the statistically anisotropic modes still persist, albeit significantly in NILC map. We further probed the data for any coherent alignments across multipoles in several bins from the chosen multipole range.
The Standard Inflationary model predicts an isotropic distribution of the Cosmic Microwave Background temperature fluctuations. Detection of deviations from statistical isotropy would call for a revision of the physics of the early universe. This paper introduces the variogram as a powerful tool to detect and characterize deviations from statistical isotropy in Cosmic Microwave Background maps. Application to the Wilkinson Microwave Anisotropy Probe data clearly shows differences between the northern and the southern hemispheres. The sill and range of the northern hemisphere's variogram are lo…
Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole and/or quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding …
Isotropy-violation statistics can highlight polarized galactic foregrounds that contaminate primordial $B$-modes in the Cosmic Microwave Background (CMB). We propose a particular isotropy-violation test and apply it to polarized Planck 353 GHz data, constructing an map that indicates $B$-mode foreground dust power over the sky. We build our main isotropy test in harmonic space via the bipolar spherical harmonic basis, and our method helps us to identify the least-contaminated directions. By this measure, there are regions of low foreground in and around the BICEP field, near the South Galactic…
The discovery of cosmic microwave background (CMB) was a paradigm shift in the study and fundamental understanding of the early universe and also the Big Bang phenomenon. Cosmic microwave background is one of the richest and intriguing sources of information available to cosmologists and one parameter of special interest is baryon density of the universe. Baryon density can be primarily estimated by analyzing CMB data or through the study of big bang nucleosynthesis(BBN). Hence, it is necessary that both of the results found though the two methods are in agreement with each other. Although the…
In recent years, there have been a large number of studies which support violation of statistical isotropy. Meanwhile, there are some studies which also found inconsistency. We use the power tensor method defined earlier in the literature to study the new CMBR data. The orientation of these three orthogonal vectors, as well as the power associated with each vector, contains information about possible violation of statistical isotropy. This information is encoded in two entropy measures, the power-entropy and alignment- entropy. We apply this method to WMAP 9-year and PLANCK data. Here, we also…
We analyse the distribution of position angles of 1 million galaxies from the Hyperleda catalogue, a sample that presents the galaxies coordinates in the celestial sphere, information that allows us to look for a possible privileged direction. Our analysis involves different tests and statistical methods, from which it is possible to infer with high probability ($p$-value extremely low) that the galactic planes are not randomly oriented in the sky. Whether this is an evidence of a cosmological anisotropy or an observational bias due to local effects is something deserving further studies.
The cumulative number count $N$, of sources above a threshold is known to approximately follow a power law behaviour $N\propto S^{-x}$. We study the variation of spectral index $x$ across the sky in order to look for possible signals of violation of isotropy. We develop a rigorous algorithm of likelihood maximisation to accurately fit for the spectral index. We divide the sky into upper and lower hemispheres for a particular choice of $z$-axis and determine the difference $Δx$ between the best fit values of the spectral indices between the two hemispheres. The maximum value of this difference …
We test the isotropy of the local distribution of galaxies using the 2MASS extended source catalogue. By decomposing the full sky survey into distinct patches and using a combination of photometric and spectroscopic redshift data, we use both parametric and non-parametric methods to obtain the shape of the luminosity function in each patch. We use the shape of the luminosity function to test the statistical isotropy of the underlying galaxy distribution. The parametric estimator shows some evidence of a hemispherical asymmetry in the north/south Galactic plane. However the non-parametric estim…
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 symmetr…
We propose a novel method for testing isotropy of a three-dimensional distribution using Shannon entropy. We test the method on some Monte Carlo simulations of isotropic and anisotropic distributions and find that the method can effectively identify and characterize different types of hemispherical asymmetry inputted in a distribution. We generate anisotropic distributions by introducing pockets of different densities inside homogeneous and isotropic distributions and find that the proposed method can effectively quantify the degree of anisotropy and determine the geometry of the pockets intro…
We analyze two volume limited galaxy samples from the SDSS photometric and spectroscopic data to test the isotropy in the local Universe. We use information entropy to quantify the global anisotropy in the galaxy distribution at different length scales and find that the galaxy distribution is highly anisotropic on small scales. The observed anisotropy diminishes with increasing length scales and nearly plateaus out beyond a length scale of 200 Mpc/h in both the datasets. We compare these anisotropies with those predicted by the mock catalogues from the N-body simulations of the Lambda CDM mode…
In this paper, we study an anisotropic universe model with Bianchi-I metric using Joint Light-curve Analysis (JLA) sample of type Ia supernovae (SNe Ia). Because light-curve parameters of SNe Ia vary with different cosmological models and SNe Ia samples, we fit the SNe Ia light-curve parameters and cosmological parameters simultaneously employing Markov Chain Monte Carlo method. Therefore, the results on the amount of deviation from isotropy of the dark energy equation of state ($δ$), and the level of anisotropy of the large-scale geometry ($Σ_0$) at present, are totally model-independent. The…
We have used the Union2.1 SNIa compilation to search for possible Hubble expansion anisotropies, dividing the sky in 9 solid angles containing roughly the same number of SNIa, as well as in the two Galactic hemispheres. We identified only one sky region, containing 82 SNIa (~15% of total sample with $z>0.02$), that indeed appears to share a significantly different Hubble expansion than the rest of the sample. However, this behavior appears to be attributed to the joint "erratic" behavior of only three SNIa and not to an anisotropic expansion. We also find that the northern and southern galacti…
We use information entropy to test the isotropy in the nearby galaxy distribution mapped by the Two Micron All-Sky redshift survey (2MRS). We find that the galaxy distribution is highly anisotropic on small scales. The radial anisotropy gradually decreases with increasing length scales and the observed anisotropy is consistent with that expected for an isotropic Poisson distribution beyond a length scale of $90 \, h^{-1}\, {\rm Mpc}$. Using mock catalogues from N-body simulations, we find that the galaxy distribution in the 2MRS exhibits a degree of anisotropy compatible with that of the $Λ$CD…
We present a new framework for testing the isotropy of the Universe using cosmic microwave background data, building on the nested-sampling ANICOSMO code. Uniquely, we are able to constrain the scalar, vector and tensor degrees of freedom alike; previous studies only considered the vector mode (linked to vorticity). We employ Bianchi type VII$_h$ cosmologies to model the anisotropic Universe, from which other types may be obtained by taking suitable limits. In a separate development, we improve the statistical analysis by including the effect of Bianchi power in the high-$\ell$, as well as the…
The two fundamental assumptions in cosmology are that the Universe is statistically homogeneous and isotropic when averaged on large scales. Given the big implication of these assumptions, there has been a lot of statistical tests carried out to verify their validity. Since the first high-precision Cosmic Microwave Background (CMB) data release by the WMAP satellite, many anomalies that challenges the isotropy assumption, including dipolar power asymmetry on large angular scales, have been reported. In this talk I will present a brief summary of the test of cosmic isotropy we carried out in th…
Testing Statistical Isotropy in the FRB Sky Distribution: A Selection-Function-Aware Framework
Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Observatório Nacional（国家天文台）；Universidade Federal Rural do Rio de Janeiro（里约热内卢联邦农村大学）；Centre of Excellence ENSEMBLE3 Sp. z o. o.（ENSEMBLE3卓越中心有限公司）
It has been argued recently by Copi etal (2009) that the lack of large angular correlations of the CMB temperature field provides strong evidence against the standard, statistically isotropic, inflationary LambdaCDM cosmology. We compare various estimators of the temperature correlation function showing how they depend on assumptions of statistical isotropy and how they perform on the WMAP 5 year ILC maps with and without a sky cut. We show that the low multipole harmonics that determine the large-scale features of the temperature correlation function can be reconstructed accurately, independe…
We probe the possible anisotropy of the Universe by using the JLA compilation of type-Ia supernovae. We apply the Markov Chain Monte Carlo (MCMC) method to constrain the amplitude and direction of anisotropy in three cosmological models. For the dipole-modulated $Λ$CDM model, the anisotropic amplitude is consistent with zero at $68\%$ C.L., and has an upper bound $A_D<1.98\times10^{-3}$ at $95\%$ C.L. Regardless of much larger uncertainty, we find the dipole direction of JLA is amazingly opposite to that of Union2. Similar results are found for the dipole-modulated $w$CDM and CPL models. Thus,…
The small but measurable effect of weak gravitational lensing on the cosmic microwave background radiation provide information about the large-scale distribution of matter in the universe. We use the all sky distribution of matter, as represented by the {\em convergence map} that is inferred from CMB lensing measurement by Planck survey, to test the fundamental assumption of Statistical Isotropy (SI) of the universe. For the analysis we use the $α$ statistic that is devised from the contour Minkowski tensor, a tensorial generalization of the scalar Minkowski functional, the contour length. In …
I introduce a simple empirical measure of average galaxy cluster sizes based on a comparison of the correlation lengths of red galaxies with blue that can provide a more accurate and bias-free measure of the average size and number density of galaxy clusters. Using 269,000 galaxies from the SDSS DR6 survey, I show that this 3D correlation length, averaged over many clusters, remains very nearly constant at L0= 4.797 +/- 0.024 Mpc/h from small redshifts out to redshifts of 0.5. This serves as a new measure of cosmic length scales and provides a means of testing the standard cosmological model t…
We analyze the magnitude-redshift data of type Ia supernovae included in the Union and Union2 compilations in the framework of an anisotropic Bianchi type I cosmological model and in the presence of a dark energy fluid with anisotropic equation of state. We find that the amount of deviation from isotropy of the equation of state of dark energy, the skewness δ, and the present level of anisotropy of the large-scale geometry of the Universe, the actual shear Σ_0, are constrained in the ranges -0.16 < δ< 0.12 and -0.012 < Σ_0 < 0.012 (1σC.L.) by Union2 data. Supernova data are then compatible wit…
A fundamental assumption in cosmology is that of statistical isotropy - that the universe, on average, looks the same in every direction in the sky. Statistical isotropy has recently been tested stringently using Cosmic Microwave Background (CMB) data, leading to intriguing results on large angular scales. Here we apply some of the same techniques used in the CMB to the distribution of galaxies on the sky. Using the multipole vector approach, where each multipole in the harmonic decomposition of galaxy density field is described by unit vectors and an amplitude, we lay out the basic formalism …
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…
We study several anisotropic inflationary models and their implications for the observed violation of statistical isotropy in the CMBR data. In two of these models the anisotropy decays very quickly during the inflationary phase of expansion. We explicitly show that these models lead to violation of isotropy only for low l CMBR modes. Our primary aim is to fit the observed alignment of l=2,3 multipoles to the theoretical models. We use two measures, based on the power tensor, which contains information about the alignment of each multipole, to quantify the anisotropy in data. One of the measur…
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 …
We present new observational constraints on inhomogeneous models based on observables independent of the CMB and large-scale structure. Using Bayesian evidence we find very strong evidence for the homogeneous LCDM model, thus disfavouring inhomogeneous models. Our new constraints are based on quantities independent of the growth of perturbations and rely on cosmic clocks based on atomic physics and on the local density of matter.
The cosmic expansion history proceeds in broad terms from a radiation dominated epoch to matter domination to an accelerated, dark energy dominated epoch. We investigate whether intermittent periods of acceleration are possible in the early universe -- between Big Bang nucleosynthesis (BBN) and recombination and beyond. We establish that the standard picture is remarkably robust: observations of anisotropies in the cosmic microwave background exclude any extra period of accelerated expansion between 1 \leq z \lesssim 10^5 (corresponding to 5\times10^{-4}\ {\rm eV} \leq T \lesssim 25\ {\rm eV})…
Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide ana…
We study the directional dependence of the angular two-point correlation function in maps of the cosmic microwave background (CMB). We propose two new statistics, one which measures the correlation of each point in the sky with a ring of points separated angle theta away, and a second that measures the missing angular correlation above 60 degrees as a function of direction. Using these statistics, we find that most of the low power in cut-sky maps measured by the WMAP experiment comes from unusually low contributions from the directions of the lobes of the quadrupole and the octupole. These fi…
Chiral gravity and cosmological birefringence both provide physical mechanisms to produce parity-violating TB and EB correlations in the cosmic microwave background (CMB) temperature/polarization. Here, we study how well these two mechanisms can be distinguished if non-zero TB/EB correlations are found. To do so, we evaluate the correlation matrix, including new TB-EB covariances. We find that the effects of these two mechanisms on the CMB are highly orthogonal, and can thus be distinguished fairly well in case of a high--signal-to-noise detection of TB/EB correlations. An Appendix evaluates t…
Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has been studied and debated extensively in recent years. Under this assumption, the hot spots and cold spots of the CMB are expected to be uniformly distributed over a 2-sphere. We use the orientation matrix, first proposed by Watson (1965) and Scheidegger (1965) and associated shape and strength parameters (Woodcock, 1977) to analyse whether the hot and cold spots of the observed CMB temperature anisotropy field are uniformly placed. We demonstrate the usefulness of our estimators by using simulated toy models containing…
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 …
There currently exist many observations which are not consistent with the cosmological principle. We review these observations with a particular emphasis on those relevant for Square Kilometre Array (SKA). In particular, several different data sets indicate a preferred direction pointing approximately towards the Virgo cluster. We also observe a hemispherical anisotropy in the Cosmic Microwave Background Radiation (CMBR) temperature fluctuations. Although these inconsistencies may be attributed to systematic effects, there remains the possibility that they indicate new physics and various theo…
Certain anomalies at large angular scales in the cosmic microwave background measured by WMAP have been suggested as possible evidence of breakdown of statistical isotropy(SI). Most CMB photons free-stream to the present from the surface of last scattering. It is thus reasonable to expect statistical isotropy violation in the CMB photon distribution observed now to have originated from SI violation in the baryon-photon fluid at last scattering, in addition to anisotropy of the primordial power spectrum studied earlier in literature. We consider the generalized anisotropic brightness distributi…
We test the statistical isotropy (SI) of the $E$-mode polarization of the cosmic microwave background (CMB) radiation observed by the Planck satellite using two statistics, namely, the contour Minkowski Tensor (CMT) and the Directional statistic ($\mathcal{D}$ statistic). The parameter $α$ obtained from the CMT provides information of the alignment of structures and can be used to infer statistical properties such as Gaussianity and SI of random fields. The $\mathcal{D}$ statistic is based on detecting preferred directionality shown by vectors defined by the field. These two tests are compleme…
In this talk we elaborate on a mechanism to generate local contributions to the curvature perturbation in isolated patches of the Cosmic Microwave Background (CMB). The mechanism, based on the generation of an out-of-equilibrium configuration in fluctuating scalar fields of mass $m\sim H$ during a sustained stage of fast-roll inflation, has been recently shown to be capable of accounting for some of the most robust large-angle anomalies detected in the CMB. In this talk, we show in detail how the embedding of the mechanism into models including vector fields can result in the breaking of stati…
Testing cosmological isotropy with gravitational waves and gamma-ray bursts
The Chinese University of Hong Kong（香港中文大学）；De La Salle University（德拉萨学院）；National University of Singapore（新加坡国立大学）；City University of Hong Kong（香港城市大学）；Chung-Ang University（中央大学）；National Tsing Hua University（国立清华大学）
Statistical isotropy (SI) of Cosmic Microwave Background (CMB) fluctuations is a key observational test to validate the cosmological principle underlying the standard model of cosmology. While a detection of SI violation would have immense cosmological ramification, it is important to recognise their possible origin in systematic effects of observations. WMAP seven year (WMAP-7) release claimed significant deviation from SI in the bipolar spherical harmonic (BipoSH) coefficients $A_{ll}^{20}$ and $A_{l-2l}^{20}$. Here we present the first explicit reproduction of the measurements reported in W…
Previous claims of significant evidence for mirror-parity in the large-scale cosmic microwave background (CMB) data from the Wilkinson Microwave Anisotropy Probe (WMAP) experiment have been recently echoed in the first study of isotropy and statistics of CMB data from Planck. We revisit these claims with a careful analysis of the latest data available. We construct statistical estimators in both harmonic and pixel space, test them on simulated data with and without mirror-parity symmetry, apply different Galactic masks, and study the dependence of the results on arbitrary choices of free param…
We use a range of cosmological data to constrain phenomenological modifications to general relativity on cosmological scales, through modifications to the Poisson and lensing equations. We include cosmic microwave background anisotropy measurements from the Planck satellite, cosmic shear from CFHTLenS and DES-SV, and redshift-space distortions from BOSS data release 12 and the 6dF galaxy survey. We find no evidence of departures from general relativity, with the modified gravity parameters constrained to $Σ_0 = 0.05^{+0.05}_{-0.07}$ and $μ_0 = -0.10^{+0.20}_{-0.16}$, where $Σ_0$ and $μ_0$ refe…
The Cosmological Principle states that the Universe is statistically isotropic and homogeneous on large scales. In particular, this implies statistical isotropy in the galaxy distribution, after removal of a dipole anisotropy due to the observer's motion. We test this hypothesis with number count maps from the NVSS radio catalogue. We use a local variance estimator based on patches of different angular radii across the sky and compare the source count variance between and within these patches. In order to assess the statistical significance of our results, we simulate radio maps with the NVSS …
The exquisitely measured maps of fluctuations in the Cosmic Microwave Background (CMB) present the possibility to test the principle of Statistical Isotropy (SI) of the Universe through systematic observable measures for non-Statistical Isotropy (nSI) features in the data. Recent measurements of the CMB temperature field provide tantalizing evidence of the deviation from SI. A systematic approach based on strong mathematical formulation allows any nSI feature to be traced to known physical effects or observational artefacts. Unexplained nSI features could have immense cosmological ramification…
The observed angular correlation function of the cosmic microwave background has previously been reported to be anomalous, particularly when measured in regions of the sky uncontaminated by Galactic emission. Recent work by Efstathiou et al. presents a Bayesian comparison of isotropic theories, casting doubt on the significance of the purported anomaly. We extend this analysis to all anisotropic Gaussian theories with vanishing mean (<delta T> = 0), using the much wider class of models to confirm that the anomaly is not likely to point to new physics. On the other hand if there is any new phys…
We present a method to test the isotropy of the magnitude-redshift relation of Type Ia Supernovae (SNe Ia) and single out the most discrepant direction (in terms of the signal-to-noise ratio) with respect to the all-sky data. Our technique accounts for possible directional variations of the corrections for SNe Ia and yields all-sky maps of the best-fit cosmological parameters with arbitrary angular resolution. To show its potential, we apply our method to the recent Union2.1 compilation, building maps with three different angular resolutions. We use a Monte Carlo method to estimate the statist…
The sky distribution of Gamma-Ray Bursts (GRBs) has been intensively studied by various groups for more than two decades. Most of these studies test the isotropy of GRBs based on their sky number density distribution. In this work we propose an approach to test the isotropy of the Universe through inspecting the isotropy of the properties of GRBs such as their duration, fluences and peak fluxes at various energy bands and different time scales. We apply this method on the {\em Fermi} / Gamma-ray Burst Monitor (GBM) data sample containing 1591 GRBs. The most noticeable feature we found is near …
We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violat…
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).…
