Search for non-Gaussianity in pixel, harmonic, and wavelet space: Compared and combined

Cabella, P.; Hansen, F. K.; Marinucci, Domenico; Pagano, Daniele; Vittorio, N.

doi:10.1103/physrevd.69.063007

Cited by 39 publications

(48 citation statements)

References 43 publications

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“…Several different groups (Gaztañaga & Wagg 2003;Mukherjee & Wang 2003;Cabella et al 2004;Phillips & Kogut 2006;Creminelli et al 2006) have applied alternative techniques to measure f NL from the maps and have similar limits on f NL . Babich et al (2004) note that these limits are sensitive to the physics that generated the non-Gaussianity as different mechanisms predict different forms for the bispectrum.…”

Section: Are Cmb Fluctuations Gaussian?mentioning

confidence: 97%

Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Implications for Cosmology

Spergel

Bean

Doré

et al. 2007

ASTROPHYS J SUPPL S

5,910

277

4,399

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A simple cosmological model with only six parameters (matter density, m h 2 , baryon density, b h 2 , Hubble constant, H 0 , amplitude of fluctuations, 8 , optical depth, , and a slope for the scalar perturbation spectrum, n s ) fits not only the 3 year WMAP temperature and polarization data, but also small-scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the bestfit values for cosmological parameters for the power-law flat Ã cold dark matter (ÃCDM) model are ( m h 2 ; b h 2 ; h; n s ; ; 8 ) ¼ (0:1277 þ0:0080 À0:0079 ;0:02229 AE 0:00073;0:732 þ0:031 À0:032 ;0:958 AE 0:016;0:089 AE 0:030; 0:761 þ0:049 À0:048 ). The 3 year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power-law spectrum, the WMAP data alone require dark matter and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n s ¼ 1; r ¼ 0). Adding additional data sets improves the constraints on these components and the spectral slope. For power-law models, WMAP data alone puts an improved upper limit on the tensor-to-scalar ratio, r 0:002 < 0:65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r 0:002 < 0:30 (95% CL). Models that suppress largescale power through a running spectral index or a large-scale cutoff in the power spectrum are a better fit to the WMAP and small-scale CMB data than the power-law ÃCDM model; however, the improvement in the fit to the WMAP data is only Á 2 ¼ 3 for 1 extra degree of freedom. Models with a running-spectral index are consistent with a higher amplitude of gravity waves. In a flat universe, the combination of WMAP and the Supernova Legacy Survey (SNLS) data yields a significant constraint on the equation of state of the dark energy, w ¼ À0:967 þ0:073 À0:072 . If we assume w ¼ À1, then the deviations from the critical density, K , are small: the combination of WMAP and the SNLS data implies k ¼ À0:011 AE 0:012. The combination of WMAP 3 year data plus the HST Key Project constraint on H 0 implies k ¼ À0:014 AE 0:017 and Ã ¼ 0:716 AE 0:055. Even if we do not include the prior that the universe is flat, by combining WMAP, large-scale structure, and supernova data, we can still put a strong constraint on the dark energy equation of state, w ¼ À1:08 AE 0:12. For a flat universe, the combination of WMAP and other astronomical data yield a constraint on the sum of the neutrino masses, P m < 0:66 eV (95%CL). Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps using Minkowski functionals, the bispectrum, trispectrum, and a new statistic designed to detect large-scale anisotropies in the fluctuations. Subject headingg s: cosmic microwave background -cosmology: observations

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Section: Are Cmb Fluctuations Gaussian?mentioning

confidence: 97%

Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Implications for Cosmology

Spergel

Bean

Doré

et al. 2007

ASTROPHYS J SUPPL S

5,910

277

4,399

View full text Add to dashboard Cite

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“…These observations have allowed precise estimates of several parameters of the greatest interest for Cosmology and Theoretical Physics. Spherical wavelets have found very extensive applications here, see for instance [8,9,25,36,37,46,49] and many others. The rationale for such a widespread interest can be explained as follows: CMB models are best analyzed in the frequency domain, where the behavior at different multipoles can be investigated separately; on the other hand, partial sky coverage and other missing observations make the evaluation of exact spherical harmonic transforms troublesome.…”

Section: Introductionmentioning

confidence: 99%

Spin Wavelets on the Sphere

Geller

Marinucci

2010

J Fourier Anal Appl

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121

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In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In particular, we propose needlet-type spin wavelets as an extension of the needlet approach recently introduced by Narcowich et al. . We discuss localization properties in the real and harmonic domains, and investigate stochastic properties for the analysis of spin random fields. Our results are strongly motivated by cosmological applications, in particular in connection to the analysis of Cosmic Microwave Background polarization data.

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“…These predictions have been extensively studied in number of works. An incomplete list includes: Abramo et al (2006); Armendariz-Picon & Pekowsky (2008); Bernui et al (2007a,b); Bielewicz et al (2005); Cabella et al (2004Cabella et al ( , 2006Cabella et al ( , 2005; Chen & Szapudi (2006a,b); Chiang et al (2003); Copi et al (2006aCopi et al ( ,b, 2004; Curto et al ( , 2008; de Oliveira-Costa & Tegmark (2006);de Troia et al (2007); Donoghue & Donoghue (2005); Efstathiou (2003); Eriksen et al (2007Eriksen et al ( , 2008Eriksen et al ( , 2004; Gaztañaga et al (2003); ; Hansen et al (2004a,b); Jaffe et al (2005); Komatsu et al (2008); Komatsu et al (2003); Land & Magueijo (2005b; Lew (2008); Lew & Roukema (2008); McEwen et al (2006); Mukherjee & Wang (2004); Naselsky et al (2005Naselsky et al ( , 2007; Park (2004); Park et al (2006); Samal et al (2008); Savage et al (2004); Shandarin (2002); Souradeep et al (2006); Vielva et al (2004); Wiaux et al (2006); Wu et al (2001); Yadav & Wandelt (2008) and references therein. Within the th...…”

Section: Introductionmentioning

confidence: 99%

Hemispherical power asymmetry: parameter estimation from cosmic microwave background WMAP5 data

Lew

2008

J. Cosmol. Astropart. Phys.

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We re-examine the evidence of hemispherical power asymmetry, detected in the cosmic microwave background (CMB) WMAP (Wilkinson Microwave Anisotropy Probe) data using a new method. We use a data filtering, preprocessing , and a statistical approach different from those used previously, and pursue an independent method of parameter estimation. First, we analyze the hemispherical variance ratios and compare these with simulated distributions. Secondly, working within a previously proposed CMB bipolar modulation model, we constrain the model parameters: the amplitude and the orientation of the modulation field as a function of various multipole bins. Finally, we select three ranges of multipoles leading to the most anomalous signals, and we process corresponding 100 Gaussian, random field (GRF) simulations, treated as observational data, to further test the statistical significance and robustness of the hemispherical power asymmetry. For our analysis we use the Internally-Linearly-Coadded (ILC) full sky map, and the KQ75 cut sky V channel foregrounds reduced map of the WMAP five year data (V5). We constrain the modulation parameters using a generic maximum a posteriori method.In particular, we find differences in hemispherical power distribution, which when described in terms of a model with bipolar modulation field, exclude the field amplitude value of the isotropic model A = 0 at confidence level of ∼ 99.5% ( ∼ 99.4%) in the multipole range ℓ ∈ [7, 19] (ℓ ∈ [7, 79]) in the V5 data, and at the confidence level ∼ 99.9% in the multipole range ℓ ∈ [7, 39] in the ILC5 data, with the best fit (modal PDF) values in these particular multipole ranges of A = 0.21 (A = 0.21) and A = 0.15 respectively.However, we also point out that similar or larger significances (in terms of rejecting the isotropic model), and large best-fit modulation amplitudes are obtained in GRF simulations as well, which reduces the overall significance of the CMB power asymmetry down to only about 94% (95%) in the V5 data, in the range ℓ ∈ [7, 19] (ℓ ∈ [7, 79]).

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Search for non-Gaussianity in pixel, harmonic, and wavelet space: Compared and combined

Cited by 39 publications

References 43 publications

Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Implications for Cosmology

Three‐YearWilkinson Microwave Anisotropy Probe(WMAP) Observations: Implications for Cosmology

Spin Wavelets on the Sphere

Hemispherical power asymmetry: parameter estimation from cosmic microwave background WMAP5 data

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