Testing Isotropy of Cosmic Microwave Background Radiation

2014

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 the latest WMAP and Planck temperature data.

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.

Journal of Cosmology and Astroparticle Physics, 2011

In this article we propose a novel test for statistical anisotropy of the CMB ∆T (n = (θ, φ)). The test is based on the fact, that the Galactic foregrounds have a remarcably strong symmetry with respect to their antipodal points S1 :=n ↔ −n,n = (θ, φ) and S2 :=n ↔n,n = π − θ, φ 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 Monte Carlo simulations. By using the analysis of the phases of the octupole we found remarkably strong cross-correlations between the phases of the kinematic dipole and the ILC 7 octupole, in full agreement with previous results. We further test the multipole range 2 < l < 100, by investigating the ratio between the l+m = even and l+m = odd parts of power spectra. We compare the results to simulations of a Gaussian random sky, and find significant departure from the statistically isotropic and homogeneous case, for a very broad range of multipoles. We found that for the most prominent peaks of our estimator, the phases of the corresponding harmonics are coherent with phases of the octupole. We believe, our test would be very useful for detections of various types of residuals of the foreground and systematic effects at a very broad range of multipoles 2 ≤ l ≤ 1500 − 3000 for the forthcoming PLANCK CMB map, before any conclusions about primordial non-Gaussianity and statistical anisotropy of the CMB.

The Astrophysical Journal, 2005

The statistical expectation values of the temperature fluctuations of the cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We use the bipolar power s pectrum (BiPS) proposed in Hajian & Souradeep to investigate the statistical isotropy (SI) of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP). The method can isolate and probe specific regions of choice in multipole space using appropriate window functions. The BiPS is estimated for full sky CMB anisotropy maps based on the first year WMAP data using a range of window functions. The BiPS spectra computed for both full sky maps for all our window functions are consistent with zero, roughly within 2 σ. The null BiPS results may be interpreted as an absence of strong violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to l ∼ 60. However, pending a careful direct comparison, our results do not necessarily conflict with the specific SI related anomalies reported using other statistical tests.

2005

The statistical expectation values of the temperature fluctuations of cosmic microwave background (CMB) are assumed to be preserved under rotations of the sky. We investigate the statistical isotropy of the CMB anisotropy maps recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP) using bipolar spherical harmonic power spectrum proposed in Hajian & Souradeep 2003. The Bipolar Power Spectrum (BiPS) is estimated for the full sky CMB anisotropy maps of the first year WMAP data. The method allows us to isolate regions in multipole space and study each region independently. This search shows no evidence for violation of statistical isotropy in the first-year WMAP data on angular scales larger than that corresponding to

Astronomy & Astrophysics, 2012

Context. Intriguing features in the angular distribution of the cosmic microwave background (CMB), such as the north-south asymmetry, were reported in the one-and three-year Wilkinson Microwave Anisotropy Probe (WMAP) data and should be studied in detail. We investigate some of these asymmetries in the CMB temperature angular distribution considering the ΛCDM model in the three, five, and seven year WMAP data. Aims. We aim to analyze the four quadrants of the internal linear combination (ILC) CMB maps using three different Galactic cuts: the WMAP KQ85 mask, a |b| < 10 • Galactic cut, and the WMAP KQ85 mask + |b| < 10 • Galactic cut. Methods. We used the two-point angular correlation function (TPCF) in the WMAP maps for each of their quadrants. The same procedure was performed for 1000 Monte Carlo (MC) simulations that were produced using the WMAP team ΛCDM best-fit power spectrum. In addition, we changed the quadrupole and octopole amplitudes obtained from the ΛCDM model spectrum. We changed this to fit the quadrupole and octopole amplitudes to their observable values from the WMAP data. We repeated the analysis for the 1000 simulations of this modified ΛCDM model, hereafter MΛCDM. Results. Our analysis showed asymmetries between the southeastern quadrant (SEQ) and the other quadrants (southwestern quadrant (SWQ), northeastern quadrant (NEQ) and northwestern quadrant (NWQ)). Over all WMAP ILC maps, the probability for the occurrence of the SEQ-NEQ, SEQ-SWQ and SEQ-NWQ asymmetries varies from 0.1% (SEQ-NEQ) to 8.5% (SEQ-SWQ) using the KQ85 mask and the KQ85 mask + |b| < 10 • Galactic cut, respectively. We also calculated the probabilities for the MΛCDM using only the KQ85 mask and found no significant differences in the results. Moreover, the cold spot region located in the SEQ quadrant was covered with masks of 5, 10 and 15 degrees radius and again the results remained unchanged. Furthermore, this analysis was repeated for random regions in the SEQ quadrant with a 15-degree mask and the SEQ quadrant still remained asymmetric with respect to the other quadrants of the CMB map. Conclusions. We found an excess of power in the TPCF at scales >100 degrees in the SEQ with respect to the other quadrants that is independent of the Galactic cut used. Moreover, we tested a possible relation between the cold spot and the SEQ excess of power and found no evidence for it. Finally, we could not find any specific region within the SEQ that might be considered responsible for the quadrant asymmetry.

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.

arXiv: Cosmology and Nongalactic Astrophysics, 2020

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 $\alpha$ 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 complementary to each other in terms of sensitivity at different angular scales. The CMT is sensitive towards small-scale information present in the CMB map while $\mathcal{D}$ statistic is more sensitive at large-scales. We compute $\alpha$ and $\mathcal{D}$ statistic for the observed $E$-mode of CMB polarization, focusing on the SMICA maps, and compare with the values calculated using FFP10 SMIC...

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

The Astrophysical Journal, 2009

We repeat and extend the analysis of Eriksen et al. and Hansen et al., testing the isotropy of the cosmic microwave background fluctuations. We find that the hemispherical power asymmetry previously reported for the largest scales ℓ = 2–40 extends to much smaller scales. In fact, for the full multipole range ℓ = 2–600, significantly more power is found in the hemisphere centered at (θ = 107° ± 10°, ϕ = 226° ± 10°) in galactic co-latitude and longitude than in the opposite hemisphere, consistent with the previously detected direction of asymmetry for ℓ = 2–40. We adopt a model selection test where the direction and amplitude of asymmetry, as well as the multipole range, are free parameters. A model with an asymmetric distribution of power for ℓ = 2–600 is found to be preferred over the isotropic model at the 0.4% significance level, taking into account the additional parameters required to describe it. A similar direction of asymmetry is found independently in all six subranges of 10...