Morphology of CMB fields—effect of weak gravitational lensing

Goyal, Priya; Chingangbam, Pravabati; Appleby, Stephen

doi:10.1088/1475-7516/2020/02/020

Cited by 14 publications

(16 citation statements)

References 76 publications

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“…This method has inherent numerical error coming from the discrete approximation of the delta function [48]. However, it was shown in [35] that the error mostly cancels out when computing α. and hence is well suited for applications where α is used to extract physical information.…”

Section: Estimator For W 1 and αmentioning

confidence: 99%

“…This analysis is a follow-up of our previous paper [35], where we carried out theoretical study of the morphology of lensed CMB fields using the CMT on ideal simulations without taking into account the real data complications like masking, noise and residual foregrounds. We quantified the distortions caused by weak lensing in the CMB hotspots and coldspots using the β parameter derived from the CMT, which is corresponding to shear.…”

Section: Introductionmentioning

confidence: 99%

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Local patch analysis for testing statistical isotropy of the Planck convergence map

Goyal,

Chingangbam

2021

Preprint

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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 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 essence, the α statistic captures the ellipticity of iso-field contours at any chosen threshold value of a smooth random field and provides a measure of anisotropy. The SI of the observed convergence map is tested against the suite of realistic simulations of the convergence map provided by the Planck collaboration. We first carry out a global analysis using the full sky data after applying the galactic and point sources mask. We find that the observed data is consistent with SI. Further we carry out a local search for departure from SI in small patches of the sky using α. This analysis reveals several sky patches which exhibit deviations from simulations with statistical significance higher than 95% confidence level (CL). Our analysis indicates that the source of the anomalous behaviour of most of the outlier patches is inaccurate estimation of noise. We identify two outlier patches which exhibit anomalous behaviour originating from departure from SI at higher than 95% CL. Most of the anomalous patches are found to be located roughly along the ecliptic plane or in proximity to the ecliptic poles.

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Section: Estimator For W 1 and αmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Local patch analysis for testing statistical isotropy of the Planck convergence map

Goyal,

Chingangbam

2021

Preprint

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“…(3.7) has inherent numerical inaccuracy [31]. However, the numerical errors for the two eigenvalues are comparable, and hence get cancelled out when we compute α, as shown in [32]. Therefore, this method is very well suited for using α to test SI.…”

Section: Minkowski Tensorsmentioning

confidence: 99%

Statistical Isotropy of the CMB E-mode signal

Kochappan,

Sen,

Ghosh

et al. 2020

Preprint

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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 (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 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 D statistic is more sensitive at large-scales. We compute α and D statistic for the observed E-mode of CMB polarization, focusing on the SMICA maps, and compare with the values calculated using FFP10 SMICA simulations which contain both CMB and noise. We find good agreement between the observed data and simulations. Further, in order to specifically analyze the CMB signal in the data, we compare the values of the two statistics obtained from the observed Planck data with the values obtained from isotropic simulations having the same power spectrum, and from SMICA noise simulations. We find no statistically significant deviation from SI using the α parameter. From D statistic we find that the data shows slight deviation from SI at large angular scales.

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“…In doing so we implicitly assume that the sampling effect in the observed data and the simulations are similar, and can be subtracted. This method has been applied to CMB temperature, E-mode and lensing convergence data from Planck [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…The threshold binning introduces numerical error in the calculation of W 1 due to the approximation of the delta function [35]. In [12] we had argued why this error is expected to be small when computing α. Here we make the argument quantitative and estimate the error as follows.…”

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confidence: 99%

The geometrical meaning of statistical isotropy of smooth random fields in two dimensions

Chingangbam,

Goyal,

Yogendran

et al. 2021

Preprint

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We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, W1, as our basic tool we first examine geometrical properties of single structures. For simple closed curves in two dimensions we show that W1 is proportional to the identity matrix if the curve has m-fold symmetry, with m ≥ 3. Then we elaborate on how W1 maps any arbitrary shaped simple closed curve to an ellipse that is unique up to translations of its centroid. We also carry out a comparison of the shape parameters, α and β, defined using W1, with the filamentarity parameter defined using two scalar Minkowski functionals -area and contour length. We show that they contain complementary shape information, with W1 containing additional information of orientation of structures. Next, we apply our method to boundaries of excursion sets of random fields and examine what statistical isotropy means for the geometry of the excursion sets. Focusing on Gaussian isotropic fields, and using a semi-numerical approach we quantify the effect of finite sampling of the field on the geometry of the excursion sets. In doing so we obtain an analytic expression for α which takes into account the effect of finite sampling. Finally we derive an analytic expression for the ensemble expectation of W1 for Gaussian anisotropic random fields. Our results provide insights that are useful for designing tests of statistical isotropy using cosmological data.

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Morphology of CMB fields—effect of weak gravitational lensing

Cited by 14 publications

References 76 publications

Local patch analysis for testing statistical isotropy of the Planck convergence map

Local patch analysis for testing statistical isotropy of the Planck convergence map

Statistical Isotropy of the CMB E-mode signal

The geometrical meaning of statistical isotropy of smooth random fields in two dimensions

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