Testing isotropy of cosmos with WMAP and PLANCK data

Rath, Pranati K.; Samal, Pramoda Kumar

doi:10.1142/s021773231550131x

Cited by 8 publications

(9 citation statements)

References 14 publications

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“…Furthermore, that work made the wrong assumption that the maximal entropy value ln(3) would be obtained for isotropic maps. The method was applied to Planck and WMAP in [42] but with the main focus on the correlation of multipoles with the quadrupole. There, no largescale anomalies were observed, but correlations with the quadrupole were found on a wider range of scales.…”

Section: Numerical Distributions At L >mentioning

confidence: 99%

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Entropy methods for CMB analysis of anisotropy and non-Gaussianity

2019

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In recent years, high-resolution cosmic microwave background (CMB) measurements have opened up the possibility to explore statistical features of the temperature fluctuations down to very small angular scales. One method that has been used is the Wehrl entropy, which is, however, extremely costly in terms of computational time. Here, we propose several different pseudoentropy measures (projection, angular, and quadratic) that agree well with the Wehrl entropy, but are significantly faster to compute. All of the presented alternatives are rotationally invariant measures of entanglement after identifying each multipole l of temperature fluctuations with a spin-l quantum state and are very sensitive to non-Gaussianity, anisotropy, and statistical dependence of spherical harmonic coefficients in the data. We provide a simple proof that the projection pseudoentropy converges to the Wehrl entropy with increasing dimensionality of the ancilla projection space. Furthermore, for l = 2, we show that both the Wehrl entropy and the angular pseudoentropy can be expressed as one-dimensional functions of the squared chordal distance of multipole vectors, giving a tight connection between the two measures. We also show that the angular pseudoentropy can clearly distinguish between Gaussian and non-Gaussian temperature fluctuations at large multipoles and henceforth provides a non-brute-force method for identifying non-Gaussianities. This allows us to study possible hints of statistical anisotropy and non-Gaussianity in the CMB up to multipole l = 1000 using Planck 2015, Planck 2018, and WMAP 7-yr full sky data. We find that l = 5 and l = 28 have a large entropy at 2-3σ significance and a slight hint towards a connection of this with the cosmic dipole. On a wider range of large angular scales we do not find indications of violation of isotropy or Gaussianity. We also find a small-scale range, l ∈ [895, 905], that is incompatible with the assumptions at about 3σ level, although how much this significance can be reduced by taking into account the selection effect, i.e.,, how likely it is to find ranges of a certain size with the observed features, and inhomogeneous noise is left as an open question. Furthermore, we find overall similar results in our analysis of the 2015 and the 2018 data. Finally, we also demonstrate how a range of angular momenta can be studied with the range angular pseudoentropy, which measures averages and correlations of different multipoles. Our main purpose in this work is to introduce the methods, analyze their mathematical background, and demonstrate their usage for providing researchers in this field with an additional tool. We believe that the formalism developed here can underpin future studies of the Gaussianity and isotropy of the CMB and help to identify deviations, especially at small angular scales.

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Section: Numerical Distributions At L >mentioning

confidence: 99%

“…(see also [41,42] for application to CMB data). In the way we have written this formula, it is now in fact no longer restricted to individual angular momentum (multipole) numbers l. It can also be applied to a range or even a selection of l: One simply needs to insert an appropriately normalized state…”

Section: A Coherent States Multipole Vectors and Entropymentioning

confidence: 99%

Entropy methods for CMB analysis of anisotropy and non-Gaussianity

2019

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“…Here we use natural units where = 1 and 8πG = c = 1. In our model the matter content of the universe will consist of the perfect fluid with a barotropic equation of state (EoS) p = ωρ (−1 < ω < +1) plus the condensate Bose-Einstein, described by the EoS (8). The energy momentum tensor is defined as…”

Section: The Classical Modelmentioning

confidence: 99%

“…It is not a simple framework but with some hyphotesis we can obtain informations about this primordial era [3][4][5]. On the other side, the SCM explains observations consistently in a simple framework but has other problems [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Primordial Universe with radiation and Bose–Einstein condensate

Alvarenga

Filho

Fracalossi

et al. 2019

Physics of the Dark Universe

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In this work we derive a scenario in which the early universe consists of radiation fluid and Bose-Einstein condensate. The possibility of gravitational self-interaction due to an attractive Bose-Einstein condensate is analyzed. The classical behavior of the scale factor of the universe is determined by a parameter associated with the Bose-Einstein fluid with bouncing or Big Crunch solutions. After we proceed to compute the finite-norm wave packet solutions to the Wheeler-DeWitt equation. The behavior of the scale factor is studied by applying the many-worlds interpretation of quantum mechanics. The quantum cosmological model is free from the singularities. PACS numbers: 98.80.-k, 98.80.Cq, 04.30.-w

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“…Statistical nature of CMB anisotropies lead to fluctuations in the eigenvalues of Power tensor about their expected value of C l /3 in a given realization. The significance of any deviation from isotropy is measured using an invariant combination of normalized eigenvalues of the Power tensor called Power entropy (Samal et al 2008(Samal et al , 2009Rath & Samal 2015).…”

Section: Introductionmentioning

confidence: 99%

Testing statistical isotropy in cosmic microwave background polarization maps

Rath

Samal

Panda

et al. 2018

Monthly Notices of the Royal Astronomical Society

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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.

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Testing isotropy of cosmos with WMAP and PLANCK data

Cited by 8 publications

References 14 publications

Entropy methods for CMB analysis of anisotropy and non-Gaussianity

Entropy methods for CMB analysis of anisotropy and non-Gaussianity

Primordial Universe with radiation and Bose–Einstein condensate

Testing statistical isotropy in cosmic microwave background polarization maps

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