Measuring statistical isotropy of CMB anisotropy

Physical Review Letters, 2016

Recent measurements of the temperature field of Cosmic Microwave Background (CMB) provide tantalising evidence for violation of Statistical Isotropy (SI) that constitutes a fundamental tenet of contemporary cosmology. CMB space based missions, WMAP and Planck have observed a 7% departure in the SI temperature field at large angular scales. However, due to higher cosmic variance at low multipoles, the significance of this measurement is not expected to improve from any future CMB temperature measurements. We demonstrate that weak lensing of the CMB due to scalar perturbations produce a corresponding SI violation in B modes of CMB polarization at smaller angular scales. Measurability of this phenomenon depends upon the scales (l range) over which power asymmetry is present. Power asymmetry which is restricted only to l < 64 in temperature field cannot lead to any significant observable effect from this new window. However, this effect can put an independent bound on the spatial range of scales of hemispherical asymmetry present in scalar sector.

Pramana, 2004

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topology. The statistical isotropy (SI) of the Cosmic Microwave Background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We propose a set of measures, κ ℓ (ℓ = 1, 2, 3, . . .) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. We numerically compute the predicted κ ℓ spectra for CMB anisotropy in flat torus universe models. Characteristic signature of different models in the κ ℓ spectrum are noted.

Monthly Notices of the Royal Astronomical Society, 2010

We test the asymmetry of the cosmic microwave background anisotropy jointly in temperature and polarization. We study the hemispherical asymmetry, previously found only in the temperature field, with respect to the axis identified by Hansen et al. To this extent, we make use of the low-resolution Wilkinson Microwave Anisotropy Probe 5-yr temperature and polarization N side = 16 maps and our implementation of an optimal power spectrum estimator. We consider two simple estimators for the power asymmetry and we compare our findings with Monte Carlo simulations which take into account the full noise covariance matrix. We confirm an excess of power in temperature angular power spectrum in the Southern hemisphere at a significant level, between 3σ and 4σ depending on the exact range of multipoles considered. We do not find significant power asymmetry in the gradient (curl) component EE (BB) of polarized angular spectra. Furthermore, cross-correlation power spectra, i.e. TE, TB, EB, show no significant hemispherical asymmetry. We also show that the cold spot found by Vielva et al. in the Southern Galactic hemisphere does not alter the significance of the hemispherical asymmetries on multipoles which can be probed by maps at resolution N side = 16. Although the origin of the hemispherical asymmetry in temperature remains unclear, the study of the polarization pattern could add useful information on its explanation. We therefore forecast by Monte Carlo the Planck capabilities in probing polarization asymmetries.

Monthly Notices of The Royal Astronomical Society, 2007

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide 2 new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated galactic plane contamination is readily identified, and the new procedures mesh perfectly with linear transformations employed for windowed-sky analysis. The ILC -WMAP data maps show 7 axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5% probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9%, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.

2013

The two fundamental assumptions of the standard cosmological model-that the initial fluctuations are statistically isotropic and Gaussian-are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the Planck satellite. The detailed results are based on studies of four independent estimates of the CMB that are compared to simulations using a fiducial ΛCDM model and incorporating essential aspects of the Planck measurement process. Deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice, and frequency dependence. Many of these anomalies were previously observed in the WMAP data, and are now confirmed at similar levels of significance (about 3σ). However, we find little evidence of non-Gaussianity, with the exception of a few statistical signatures that seem to be associated with specific anomalies. In particular, we find that the quadrupole-octopole alignment is also connected to a low observed variance in the CMB signal. A power asymmetry is now found to persist on scales corresponding to about = 600 and can be described in the low-regime by a phenomenological dipole modulation model. However, any primordial power asymmetry is strongly scale-dependent and does not extend to arbitrarily small angular scales. Finally, it is plausible that some of these features may be reflected in the angular power spectrum of the data, which shows a deficit of power on similar scales. Indeed, when the power spectra of two hemispheres defined by a preferred direction are considered separately, one shows evidence of a deficit in power, while its opposite contains oscillations between odd and even modes that may be related to the parity violation and phase correlations also detected in the data. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking.

The Astrophysical Journal, 2004

We report on the results from two independent but complementary statistical analyses of the WMAP first-year data, based on the power spectrum and N-point correlation functions. We focus on large and intermediate scales (larger than about 3 •) and compare the observed data against Monte Carlo ensembles with WMAP-like properties. In both analyses, we measure the amplitudes of the large-scale fluctuations on opposing hemispheres and study the ratio of the two amplitudes. The power-spectrum analysis shows that this ratio for WMAP, as measured along the axis of maximum asymmetry, is high at the 95%-99% level (depending on the particular multipole range included). The axis of maximum asymmetry of the WMAP data is weakly dependent on the multipole range under consideration but tends to lie close to the ecliptic axis. In the N-point correlation function analysis we focus on the northern and southern hemispheres defined in ecliptic coordinates, and we find that the ratio of the large-scale fluctuation amplitudes is high at the 98%-99% level. Furthermore, the results are stable with respect to choice of Galactic cut and also with respect to frequency band. A similar asymmetry is found in the COBE-DMR map, and the axis of maximum asymmetry is close to the one found in the WMAP data. Subject headings: cosmic microwave background-cosmology: observations-methods: statistical

Physical Review D, 2015

The Astrophysical Journal, 2004

We cross-correlate the cosmic microwave background temperature anisotropy maps from the WMAP, MAXIMA-I, and MAXIMA-II experiments. We use the cross-spectrum, which is the spherical harmonic transform of the angular two-point correlation function, to quantify the correlation as a function of angular scale. We find that the three possible pairs of cross-spectra are in close agreement with each other and with the power spectra of the individual maps. The probability that there is no correlation between the maps is smaller than 1 × 10 −8. We also calculate power spectra for maps made of differences between pairs of maps, and show that they are consistent with no signal. The results conclusively show that the three experiments not only display the same statistical properties of the CMB anisotropy, but also detect the same features wherever the observed sky areas overlap. We conclude that the contribution of systematic errors to these maps is negligible and that MAXIMA and WMAP have accurately mapped the cosmic microwave background anisotropy.

Journal of Cosmology and Astroparticle Physics

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 non-uniform data. We apply our method on several foreground minimized CMB maps observed by WMAP and Planck over large angular scales. The shape and strength parameters constrain geometric features of possible deviations from uniformity (isotropy) and the power of the anomalous signal. We find that distributions of hot or cold spots in cleaned maps show no unusual signature of clustering or gir...

2019

Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the ΛCDM cosmological model, yet also confirm the presence of several so-called &quot;anomalies&quot; on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, Q and U, or the E-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some ...

The Astrophysical Journal, 1995

We detect anisotropy in the cosmic microwave background (CMB) at degree angular scales and confirm a previous detection reported by . The root-mean-squared amplitude of the fluctuations is 44 +13 −7 µK. This may be expressed as the square root of the angular power spectrum in a band of multipoles between l ef f = 69 +29 −22 . We find δT l = l(2l + 1) < |a m l | 2 > /4π = 42 +12 −7 µK. The measured spectral index of the fluctuations is consistent with zero, the value expected for the CMB. The spectral index corresponding to Galactic free-free emission, the most likely foreground contaminant, is rejected at approximately 3σ.

Space Sciences Series of ISSI, 2002

This paper discusses the status of observations of Cosmic Microwave Background (CMB) anisotropies. The first detections of primary anisotropies in the CMB, achieved about 10 years ago, boosted a large number of ground-based and balloon-borne experiments that have delineated the CMB angular power spectrum up to spherical harmonic multipole ∼ 1000. A wealth of information on cosmological parameters is being revealed by these measurements. Very recently, the positions and amplitudes of the first and second peak in the power spectrum have been determined providing strong support to inflationary models with adiabatic primordial density perturbations. A total density equal to the critical value, and baryonic density consistent with Big Bang nucleosynthesis are the first results emerging from the current CMB data. Future experiments on ground (mainly interferometers), in balloons and from space (MAP and Planck missions) have the potential to constrain more than 10 cosmological parameters with high precision.

2003

The breakdown of statistical homogeneity and isotropy of cosmic perturbations is a generic feature of ultra large scale structure of the cosmos, in particular, of non trivial cosmic topology. The statistical isotropy (SI) of the Cosmic Microwave Background temperature fluctuations (CMB anisotropy) is sensitive to this breakdown on the largest scales comparable to, and even beyond the cosmic horizon. We study a set of measures, κ ℓ (ℓ = 1, 2, 3, . . .) which for non-zero values indicate and quantify statistical isotropy violations in a CMB map. The main goal here is to interpret the κ ℓ spectrum and relate it to characteristic patterns in the correlation function of CMB anisotropy arising from cosmic topology. We numerically compute the predicted κ ℓ spectrum for CMB anisotropy in flat torus universe models. The essential features are captured in the leading order approximation to the correlation function where κ ℓ can be calculated analytically. The κ ℓ spectrum is shown to reflect the number, importance and relative orientation of principal directions in the CMB correlation dictated by the shape of the Dirichlet domain (DD) of the compact space and its size relative to cosmic horizon. Hence, besides detecting cosmic topology, κ ℓ can discriminate between different topology of the universe complementing ongoing search for cosmic topology in CMB anisotropy data.

The Astrophysical Journal, 1997

We report on a measurement of the angular power spectrum of the anisotropy in the Cosmic Microwave Background. The anisotropy is measured in 23 different multipole bands from ℓ = 54 (≈ 3 • ) to ℓ = 404 (≈ 0.45 • ) and in 6 frequency bands from 26 GHz to 46 GHz over three observing seasons. The measurements are consistent from year to year. The frequency spectral index of the fluctuations (measured at low ℓ) is consistent with that of the CMB and inconsistent with either dust or Galactic free-free emission. Furthermore, the observations of the MSAM1-92 experiment ) are repeated and confirmed. The angular spectrum shows a distinct rise from δT ℓ ≡ ℓ(2ℓ + 1) < |a m ℓ | 2 > /4π = 49 +8 −5 µK at ℓ = 87 to δT ℓ = 85 +10 −8 µK at ℓ = 237. These values do not include an overall ±14% (1σ) calibration uncertainty. The analysis and possible systematic errors are discussed.

The Astrophysical Journal, 1993

We report a measurement of anisotropy in the cosmic microwave background radiation (CMBR) on 7@È22@ scales. Observations of 36 Ðelds near the North Celestial Pole (NCP) were made at 31.7 and 14.5 GHz, using the 5.5 m and 40 m telescopes at the Owens Valley Radio Observatory (OVRO) from 1993 to 1996. Multiepoch VLA observations at 8.5 and 15 GHz allow removal of discrete source contamination. After point-source subtraction, we detected signiÐcant structure, which we identify with emission from a combination of a steep-spectrum foreground and the CMBR. The foreground component is found to correlate with IRAS 100 km dust emission. Lack of Ha emission near the NCP suggests that this foreground is either high-temperature thermal bremsstrahlung K), Ñat-spectrum synchro-(T e Z 106 tron, or an exotic component of dust emission. On the basis of low-frequency maps of the NCP, we can restrict the spectral index of the foreground to b º [2.2. Although the foreground signal dominates at 14.5 GHz, the extracted CMBR component contributes 88% of the variance at 31.7 GHz, yielding an rms Ñuctuation amplitude of kK, including 4.3% calibration uncertainty and 12% sample 82~9 .1 12.1 variance (68% conÐdence). In terms of the angular power spectrum, averaged over a range C l \ S o a l m o2T, of multipoles l \ 361È756, the detected broadband amplitude is kK. dT le 4 [l(l ] 1)C l /(2n)]1@2 \ 59~6 .5 8.6 This measurement, when combined with small angular scale upper limits obtained at the OVRO, indicates that the CMBR angular power spectrum decreases between l D 600 and l D 2000 and is consistent with Ñat cosmological models. Subject headings : cosmic microwave background È cosmology : observations