Journal of Fourier Analysis and Applications

, Volume 13, Issue 4, pp 495–510 | Cite as

Cosmological Applications of a Wavelet Analysis on the Sphere

  • J.D. McEwen
  • P. Vielva
  • Y. Wiaux
  • R.B. Barreiro
  • L. Cayón
  • M.P. Hobson
  • A.N. Lasenby
  • E. Martínez-González
  • J.L. Sanz


The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerful techniques available to cosmologists for placing strong constraints on the cosmological parameters that describe the origin, content and evolution of the Universe. The last decade has witnessed the introduction of wavelet analyses in cosmology and, in particular, their application to the CMB. We review here spherical wavelet analyses of the CMB that test the standard cosmological concordance model. The assumption that the temperature anisotropies of the CMB are a realisation of a statistically isotropic Gaussian random field on the sphere is questioned. Deviations from both statistical isotropy and Gaussianity are detected in the reviewed works, suggesting more exotic cosmological models may be required to explain our Universe. We also review spherical wavelet analyses that independently provide evidence for dark energy, an exotic component of our Universe of which we know very little currently. The effectiveness of accounting correctly for the geometry of the sphere in the wavelet analysis of full-sky CMB data is demonstrated by the highly significant detections of physical processes and effects that are made in these reviewed works.


Dark Energy Wavelet Analysis Cosmic Microwave Background Wilkinson Microwave Anisotropy Probe Cosmological Application 
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Copyright information

© Birkhauser Boston 2007

Authors and Affiliations

  1. 1.Astrophysics Group, Cavendish Laboratory, University of CambridgeCambridge CB3 0HEUnited Kingdom
  2. 2.Instituto de Física de Cantabria (CSIC-UC)E-39005 SantanderSpain
  3. 3.Signal Processing Institute, Ecole Polytechnique Fédérale de Lausanne(EPFL)CH-1015 LausanneSwitzerland
  4. 4.Department of Physics, Purdue University, 525 Northwestern AvenueWest Lafayette, IN 47907-2036USA

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