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Scaling Indices Applied to the WMAP 5-Year Data

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Non-linear Data Analysis on the Sphere

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Abstract

We continue the analysis of non-Gaussianities in the CMB by means of the scaling index method (SIM, Räth, Schuecker and Banday 2007) by applying this method on the single Q-, V-, W-bands and the co-added VW-band of the 5-year data of the Wilkinson Microwave Anisotropy Probe (WMAP). We compare each of the results with 1000 Monte Carlo simulations mimicking the Gaussian properties of the best fit \(\Lambda CDM\)-model. Based on the scaling indices, scale-dependent empirical probability distributions, moments of these distributions and \(\chi ^2\)-combinations of them are calculated, obtaining similar results as in the former analysis of the 3-year data: We derive evidence for non-Gaussianity with a probability of up to 97.3 % for the mean when regarding the KQ75-masked full sky and summing up over all considered length scales by means of a diagonal \(\chi ^2\)-statistics. Looking at only the northern or southern hemisphere of the galactic coordinate system, we obtain up to 98.5 or 96.6 %, respectively. For the standard deviation, these results appear as 95.6 % for the full sky (99.7 % north, 89.4 % south) and for a \(\chi ^2\)-combination of both measurements as 97.4 % (99.1 % north, 95.5 % south). We obtain larger deviations from Gaussianity when looking at separate scale lengths. By performing an analysis of rotated hemispheres, we detect an obvious asymmetry in the data. In addition to these investigations, we present a method of filling the mask with Gaussian noise to eliminate boundary effects caused by the mask. With the help of this technique, we identify several local features on the map, of which the most significant one turns out to be the well-known cold spot. When excluding all these spots from the analysis, the deviation from Gaussianity increases, which shows that the discovered local anomalies are not the reason of the global detection of non-Gaussianity, but actually were damping the deviations on average. Our analyses per band and per year suggest, however, that it is very unlikely that the detected anomalies are due to foreground effects.

Original publication: G. Rossmanith, C. Räth, A. J. Banday and G. Morfill, Non-Gaussian Signatures in the five-year WMAP data as identified with isotropic scaling indices, MNRAS, 399, 1921 (2009)

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Notes

  1. 1.

    http://lambda.gsfc.nasa.gov

  2. 2.

    http://healpix.jpl.nasa.gov

  3. 3.

    http://lambda.gsfc.nasa.gov

References

  1. A.H. Guth, Phys. Rev. D 23, 347 (1981)

    Article  ADS  Google Scholar 

  2. A. Linde, Phys. Lett. 108B, 389 (1982)

    MathSciNet  ADS  Google Scholar 

  3. A. Albrecht, P. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982)

    Article  ADS  Google Scholar 

  4. V. Acquaviva, N. Bartolo, S. Matarrese, A. Riotto, Nucl. Phys. B 667, 119 (2003)

    Article  ADS  MATH  Google Scholar 

  5. A.H. Linde, V. Mukhanov, Phys. Rev. D 56, R535 (1997)

    Article  ADS  Google Scholar 

  6. P.J.E. Peebles, ApJ Lett. 438, L1 (1997)

    Article  ADS  Google Scholar 

  7. F. Bernardeau, J.-P. Uzan, Phys. Rev. D 66, 103506 (2002)

    Article  ADS  Google Scholar 

  8. N. Bartolo, S. Matarrese, A. Riotto, Phys. Rev. D 65, 103505 (2002)

    Article  ADS  Google Scholar 

  9. D.H. Lyth, D. Wands, Phys. Lett. B 524, 5 (2002)

    Article  ADS  MATH  Google Scholar 

  10. D.H. Lyth, C. Ungarelli, D. Wands, Phys. Rev. D 67, 023503 (2003)

    Article  ADS  Google Scholar 

  11. J. Garriga, V. Mukhanov, Phys. Lett. B 458, 219 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. C. Armendariz-Picon, T. Damour, V. Mukhanov, Phys. Lett. B 458, 209 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. N. Bartolo, E. Komatsu, S. Matarrese, A. Riotto, Phys. Rep. 402, 103 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  14. M. LoVerde, A. Miller, S. Shandera, L. Verde, JCAP 4, 14 (2008)

    Article  ADS  Google Scholar 

  15. N. Kaiser, A. Stebbins, Nature 310, 391 (1984)

    Article  ADS  Google Scholar 

  16. N. Turok, D. Spergel, Phys. Rev. Lett. 64, 2736 (1990)

    Article  ADS  Google Scholar 

  17. N. Turok, ApJ Lett. 473, L5 (1996)

    Article  ADS  Google Scholar 

  18. R. Jeannerot, J. Rocher, M. Sakellariadou, Phys. Rev. D 68, 103514 (2003)

    Article  ADS  Google Scholar 

  19. E. Komatsu, N. Afshordi, N. Bartolo, D. Baumann, J.R. Bond, E.I. Buchbinder, C.T. Byrnes, X. Chen, D.J.H. Chung, A. Cooray, P. Creminelli, N. Dalal, O. Dore, R. Easther, A.V. Frolov, K.M. Górski, M.G. Jackson, J. Khoury, W.H. Kinney, L. Kofman, K. Koyama, L. Leblond, J.-L. Lehners, J.E. Lidsey, M. Liguori, E.A. Lim, A. Linde, D.H. Lyth, J. Maldacena, S. Matarrese, L. McAllister, P. McDonald, S. Mukohyama, B. Ovrut, H.V. Peiris, C. Raeth, A. Riotto, Y. Rodriguez, M. Sasaki, R. Scoccimarro, D. Seery, E. Sefusatti, U. Seljak, L. Senatore, S. Shandera, E.P.S. Shellard, E. Silverstein, A. Slosar, K.M. Smith, A.A. Starobinsky, P.J. Steinhardt, F. Takahashi, M. Tegmark, A.J. Tolley, L. Verde, B.D. Wandelt, D. Wands, S. Weinberg, M. Wyman, A.P.S. Yadav, M. Zaldarriaga, Astro2010, The Astronomy and Astrophysics Decadal Survey. Science White Papers 158 (2009)

    Google Scholar 

  20. L.-Y. Chiang, P.D. Naselsky, O.V. Verkhodanov, M.J. Way, ApJ Lett. 590, L65 (2003)

    Article  ADS  Google Scholar 

  21. E. Komatsu, A. Kogut, M.R. Nolta, C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, M. Limon, S.S. Meyer, L. Page, D.N. Spergel, G.S. Tucker, L. Verde, E. Wollack, E.L. Wright, ApJS 148, 119 (2003)

    Article  ADS  Google Scholar 

  22. P. Coles, P. Dineen, J. Earl, D. Wright, MNRAS 350, 989 (2004)

    Article  ADS  Google Scholar 

  23. I.J. O’Dwyer, H.K. Eriksen, B.D. Wandelt, J.B. Jewell, D.L. Larson, K.M. Górski, A.J. Banday, S. Levin, P.B. Lilje, ApJ Lett. 617, L99 (2004)

    Article  ADS  Google Scholar 

  24. L.-Y. Chiang, P.D. Naselsky, P. Coles, ApJ 664, 8 (2007)

    Article  ADS  Google Scholar 

  25. H.K. Eriksen, G. Huey, A.J. Banday, K.M. Górski, J.B. Jewell, I.J. O’Dwyer, B.D. Wandelt, ApJ 665, 1L (2007)

    Article  ADS  Google Scholar 

  26. O. Rudjord, F.K. Hansen, X. Lan, M. Liguori, D. Marinucci, S. Matarrese, ApJ 701, 369 (2009)

    Article  ADS  Google Scholar 

  27. K.M. Smith, L. Senatore, M. Zaldarriaga, JCAP 0909, 006 (2009)

    Article  ADS  Google Scholar 

  28. H.K. Eriksen, F.K. Hansen, A.J. Banday, K.M. Górski, P.B. Lilje, ApJ 605, 14 (2004)

    Article  ADS  Google Scholar 

  29. F.K. Hansen, A.J. Banday, K.M. Górski, MNRAS 354, 641 (2004)

    Article  ADS  Google Scholar 

  30. F.K. Hansen, A.J. Banday, K.M. Górski, H.K. Eriksen, P.B. Lilije, ApJ 704, 1448 (2009)

    Article  ADS  Google Scholar 

  31. A. Bonaldi, S. Ricciardi, S. Leach, F. Stivoli, C. Baccigalupi, G. De Zotti, MNRAS 382, 1791 (2007)

    Article  ADS  Google Scholar 

  32. A. Bernui, Phys. Rev. D 78, 063531 (2008)

    Article  ADS  Google Scholar 

  33. A. Bernui, W.S. Hipolito-Ricaldi, MNRAS 389, 1453 (2008)

    Article  ADS  Google Scholar 

  34. J. Hoftuft, H.K. Eriksen, A.J. Banday, K.M. Górski, F.K. Hansen, P.B. Lilje, ApJ 699, 985 (2009)

    Article  ADS  Google Scholar 

  35. H.K. Eriksen, D.I. Novikov, P.B. Lilje, A.J. Banday, K.M. Górski, ApJ 612, 64 (2004)

    Article  ADS  Google Scholar 

  36. C.-G. Park, MNRAS 349, 313 (2004)

    Article  ADS  Google Scholar 

  37. P. Vielva, E. Martínes-González, R.B. Barreiro, J.L. Sanz, L. Cayón, ApJ 609, 22 (2004)

    Article  ADS  Google Scholar 

  38. F.K. Hansen, P. Cabella, D. Marinucci, N. Vittorio, ApJ Lett. 607, L67 (2004)

    Article  ADS  Google Scholar 

  39. K. Land, J. Magueijo, MNRAS 357, 994 (2005)

    Article  ADS  Google Scholar 

  40. D. Pietrobon, A. Amblard, A. Balbi, P. Cabella, A. Cooray, D. Marinucci, Phys. Rev. D 78, 103504 (2008)

    Article  ADS  Google Scholar 

  41. C. Räth, G. Morfill, G. Rossmanith, A.J. Banday, K.M. Gorski, PRL 102, 131301 (2009)

    Article  ADS  Google Scholar 

  42. V.G. Gurzadyan, A.A. Kocharyan, A &A Lett. 492, L33 (2008)

    ADS  Google Scholar 

  43. V.G. Gurzadyan, A.E. Allahverdyan, T. Ghahramanyan, A.L. Kashin, H.G. Khachatryan, A.A. Kocharyan, H. Kuloghlian, S. Mirzoyan, E. Poghosian, G. Yegorian, A &A 497, 343 (2009)

    ADS  Google Scholar 

  44. P. Mukherjee, Y. Wang, ApJ 613, 51 (2004)

    Article  ADS  Google Scholar 

  45. L. Cayón, L. Jin, A. Treaster, MNRAS 362, 826 (2005)

    Article  ADS  Google Scholar 

  46. M. Cruz, E. Martínes-González, P. Vielva, L. Cayón, MNRAS 356, 29 (2005)

    Article  ADS  Google Scholar 

  47. M. Cruz, L. Cayón, E. Martínes-González, P. Vielva, J. Jin, ApJ 655, 11 (2007)

    Article  ADS  Google Scholar 

  48. J.D. McEwen, M.P. Hobson, A.N. Lasenby, D.J. Mortlock, MNRAS 359, 1583 (2005)

    Article  ADS  Google Scholar 

  49. J.D. McEwen, M.P. Hobson, A.N. Lasenby, D.J. Mortlock, MNRAS Lett. 371, L50 (2006)

    ADS  Google Scholar 

  50. J.D. McEwen, M.P. Hobson, A.N. Lasenby, D.J. Mortlock, MNRAS 388, 659 (2008)

    Article  ADS  Google Scholar 

  51. P. Vielva, Y. Wiaux, E. Martínes-González, P. Vandergheynst, MNRAS 381, 932 (2007)

    Article  ADS  Google Scholar 

  52. C. Räth, P. Schuecker, A.J. Banday, MNRAS 380, 466 (2007)

    Article  ADS  Google Scholar 

  53. G. Hinshaw, M.R. Nolta, C.L. Bennett, R. Bean, O. Dor, M.R. Greason, M. Halpern, R.S. Hill, N. Jarosik, A. Kogut, E. Komatsu, M. Limon, N. Odegard, S.S. Meyer, L. Page, H.V. Peiris, D.N. Spergel, G.S. Tucker, L. Verde, J.L. Weiland, E. Wollack, E.L. Wright, ApJS 170, 288 (2007)

    Article  ADS  Google Scholar 

  54. L. Page, G. Hinshaw, E. Komatsu, M.R. Nolta, D.N. Spergel, C.L. Bennett, C. Barnes, R. Bean, O. Dor, J. Dunkley, M. Halpern, R.S. Hill, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, N. Odegard, H.V. Peiris, G.S. Tucker, L. Verde, J.L. Weiland, E. Wollack, E.L. Wright, ApJS 170, 335 (2007)

    Article  ADS  Google Scholar 

  55. C.L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S.S. Meyer, L. Page, D.N. Spergel, G.S. Tucker, E. Wollack, E.L. Wright, C. Barnes, M.R. Greason, R.S. Hill, E. Komatsu, M.R. Nolta, N. Odegard, H.V. Peirs, L. Verde, J.L. Weiland, ApJS 148, 1 (2003)

    Article  ADS  Google Scholar 

  56. G. Hinshaw, J.L. Weiland, R.S. Hill, N. Odegard, D. Larson, C.L. Bennett, J. Dunkley, B. Gold, M.R. Greason, N. Jarosik, E. Komatsu, M.R. Nolta, L. Page, D.N. Spergel, E. Wollack, M. Halpern, A. Kogut, M. Limon, S.S. Meyer, G.S. Tucker, E.L. Wright, ApJS 180, 225 (2009)

    Article  ADS  Google Scholar 

  57. K.M. Górski, E. Hivon, A.J. Banday, B.D. Wandelt, F.K. Hansen, M. Reinecke, M. Bartelmann, ApJ 622, 759 (2005)

    Article  ADS  Google Scholar 

  58. B. Gold, C.L. Bennett, R.S. Hill, G. Hinshaw, N. Odegard, L. Page, D.N. Spergel, J.L. Weiland, J. Dunkley, M. Halpern, N. Jarosik, A. Kogut, E. Komatsu, D. Larson, S.S. Meyer, M.R. Nolta, E. Wollack, E.L. Wright, ApJ Suppl. Ser. 180, 265 (2009)

    Article  ADS  Google Scholar 

  59. C. Räth, W. Bunk, M.B. Huber, G.E. Morfill, J. Retzla, P. Schuecker, MNRAS 337, 413 (2002)

    Google Scholar 

  60. C. Räth, P. Schuecker, MNRAS 344, 115 (2003)

    Google Scholar 

  61. M. Gliozzi, W. Brinkmann, C. Räth, I.E. Papadakis, H. Negoro, H. Scheingraber, A &A 391, 875 (2002)

    ADS  Google Scholar 

  62. M. Gliozzi, I.E. Papadakis, C. Räth, A &A 449, 969 (2006)

    ADS  Google Scholar 

  63. F. Jamitzky, R.W. Stark, W. Bunk, S. Thalhammer, C. Räth, T. Aschenbrenner, G.E. Morfill, W.M. Heckl, Ultramicroscopy 86, 241 (2001)

    Article  Google Scholar 

  64. R. Monetti, H. Böhm, D. Müller, D. Newitt, S. Majumdar, E. Rummeny, T.M. Link, C. Räth, Proc. SPIE 5032, 1777 (2003)

    Article  ADS  Google Scholar 

  65. C. Räth, R. Monetti, J. Bauer, I. Sidorenko, D. Müller, M. Matsuura, E.-M. Lochmüller, P. Zysset, F. Eckstein, New J. Phys. 10, 125010 (2008)

    Article  Google Scholar 

  66. K. Tomita, Phys. Rev. D 72, 10 (2005)

    Google Scholar 

  67. K. Tomita, K.T. Inoue, Phys. Rev. D 77, 103522 (2008)

    Article  ADS  Google Scholar 

  68. R.J. Adler, J.D. Bjorken, J.M. Overduin, gr-qc/0602102 (2006)

    Google Scholar 

  69. K.T. Inoue, J. Silk, ApJ 648, 23 (2006)

    Article  ADS  Google Scholar 

  70. K.T. Inoue, J. Silk, ApJ 664, 650 (2007)

    Article  ADS  Google Scholar 

  71. L. Rudnick, S. Brown, L. Williams, ApJ 671, 40 (2007)

    Article  ADS  Google Scholar 

  72. B.R. Granett, M.C. Neyrinck, I. Szapudi, ApJ 683, L99 (2008)

    Article  ADS  Google Scholar 

  73. M. Cruz, N. Turok, P. Vielva, E. Martínes-González, M. Hobson, Science 318, 1612 (2007)

    Article  ADS  Google Scholar 

  74. P.D. Naselsky, P.R. Christensen, P. Coles, O. Verkhodanov, D. Novikov, J. Kim, Astrophys. Bull. 65, 101 (2010)

    Article  ADS  Google Scholar 

  75. R.A. Battye, B. Garbrecht, A. Pilaftsis, JCAP 809, 20 (2008)

    ADS  Google Scholar 

  76. J.A.R. Cembranos, A. de la Cruz-Dombriz, A. Dobado, A.L. Maroto, arXiv:0803.0694 (2008)

    Google Scholar 

  77. J. Garcia-Bellido, T. Haugbolle, JCAP 04, 003 (2008)

    Article  ADS  Google Scholar 

  78. I. Masina, A. Notari, JCAP 09, 028 (2010)

    Article  ADS  Google Scholar 

  79. Y. Wiaux, P. Vielva, R.B. Barreiro, E. Martínes-González, P. Vandergheynst, MNRAS 385, 939 (2008)

    Article  ADS  Google Scholar 

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  1. Max-Planck-Institute for Extraterrestrial Physics, Max Planck Society, Giessenbachstrasse 1, 85748, Garching, Germany

    Gregor Rossmanith

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Rossmanith, G. (2013). Scaling Indices Applied to the WMAP 5-Year Data. In: Non-linear Data Analysis on the Sphere. Springer Theses. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00309-2_4

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