arXiv: Cosmology and Nongalactic Astrophysics, 2019
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of p... more 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). If the field is {isotropic and Gaussian} then the probe coefficients for a given direction should be realisations of uncorrelated scalar Gaussian random variables. We find that for most of the maps there are many directions for which this is not the case. We make a first attempt at justifying the features of the temperature maps that contribute to the apparent lack of randomness. In the case o...
We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of p... more We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of purported isotropic Gaussian random fields on the sphere. If the field is isotropic and Gaussian then the probe coefficients for a given direction should be realizations of uncorrelated scalar Gaussian random variables. To study the randomness of a field, we use the autocorrelation of the sequence of probe coefficients (which are just the Fourier coefficients [Formula: see text] if the [Formula: see text]-axis is taken in the probe direction). We introduce a particular function on the sphere (called the AC discrepancy) that accentuates the departure from Gaussianity and isotropy. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the Planck collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. We find that for some of the maps, there are many directions for which the departures are significant, especially...
arXiv: Cosmology and Nongalactic Astrophysics, 2019
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of p... more 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). If the field is {isotropic and Gaussian} then the probe coefficients for a given direction should be realisations of uncorrelated scalar Gaussian random variables. We introduce a particular function on the sphere (called the \emph{AC discrepancy}) that accentuates the departure from Gaussianity and isotropy. We find that for some of the maps, there are many directions for which the departures ...
arXiv: Cosmology and Nongalactic Astrophysics, 2019
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of p... more 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). If the field is {isotropic and Gaussian} then the probe coefficients for a given direction should be realisations of uncorrelated scalar Gaussian random variables. We find that for most of the maps there are many directions for which this is not the case. We make a first attempt at justifying the features of the temperature maps that contribute to the apparent lack of randomness. In the case o...
We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of p... more We introduce a new mathematical tool (a direction-dependent probe) to analyze the randomness of purported isotropic Gaussian random fields on the sphere. If the field is isotropic and Gaussian then the probe coefficients for a given direction should be realizations of uncorrelated scalar Gaussian random variables. To study the randomness of a field, we use the autocorrelation of the sequence of probe coefficients (which are just the Fourier coefficients [Formula: see text] if the [Formula: see text]-axis is taken in the probe direction). We introduce a particular function on the sphere (called the AC discrepancy) that accentuates the departure from Gaussianity and isotropy. We apply the probe to assess the full-sky cosmic microwave background (CMB) temperature maps produced by the Planck collaboration (PR2 2015 and PR3 2018), with special attention to the inpainted maps. We find that for some of the maps, there are many directions for which the departures are significant, especially...
arXiv: Cosmology and Nongalactic Astrophysics, 2019
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of p... more 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). If the field is {isotropic and Gaussian} then the probe coefficients for a given direction should be realisations of uncorrelated scalar Gaussian random variables. We introduce a particular function on the sphere (called the \emph{AC discrepancy}) that accentuates the departure from Gaussianity and isotropy. We find that for some of the maps, there are many directions for which the departures ...
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