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Beyond the Concordance Model - PiTP

Beyond the Concordance Model - PiTP

Frequentist approch →

Frequentist approch → the Bispectrum a natural follow on from the Power Spectrum. Expression of temperature fluctuations of the CMB on the celestial sphere, in terms of an expansion in spherical harmonics: ∆T T (α, φ) = ∞ ∑ l∑ l=2 m=−l a lm Y lm (α, φ) where (α, φ) are the polar coordinates of a point on the spherical surface. The angular power spectrum → C l = 〈|a lm | 2 〉 The Bispectrum → 〈B m 1m 2 m 3 l 1 l 2 l 3 〉 ≡ 〈a l1 m 1 a l2 m 2 a l3 m 3 〉 The harmonic transform of the 3-point correlation function → gives a scale-dependent measure of skewness → it ensemble averages to zero for Gaussian fluctuations. For VSA experiment → use the flat sky approximation. (Smith et al., 2003)

VSA1G: B(l l l) 0.0015 1σ 2σ data 0.001 B / µK 3 0.0005 0 -0.0005 -0.001 -0.0015 400 600 800 1000 1200 1400 l Diagonal bispectrum estimate with variance from Gaussian simulations for compact array field VSA1G. Conclusion → No Non-Gaussianity Yet!

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