Non-Gaussianity at low and high multipoles from WMAP data Oleg Verkhodanov Special astrophysical observatory Nizhnij Arkhyz, Russia A.G.Doroshkevich, P.D.Naselsky, I.D.Novikov, L.-Y. Chiang

Analysis of CMB data Registration: time odered data Pixelization: data accumuation in pixels Component separation Analysis of signal statistics Analysis of power spectrum

Multipole expansion L = 2 (quadrupole) L =3 (octupole) L = 5 L = 4

To the problem modern history of CMB Gaussianty All the data are Gaussian: WMAP team (Komatsu et al., 2003), Tegmark et al. (2003), and Spanish team with wavelets, WMAP3 (Spergel, et al., 2006) Detection of non-Gaussianity Chiang, Naselsky, Verkhodanov, Way (2003) – phase analysis Confirmation: Dineen, Coles (2003) – phase analysis Spanish (Vielva, Martinez-Gonzales et al., 2003) – wavelet analysis Erikson et al, 2003 – Mikowski functionals and so on...

Foregrounds + systematic NON-GAUSSIANITY Primordial Foregrounds + systematic NEW PHYSICS S= G + NG

Why Gaussianity of signal is important ? Test for the standard (now) simple inflational LCDM model. Non-Gaussianity: Complex inflation Topological: close Universe (non-trivial topology), topological defects (strings), fractals Systematic (effect of observations and analysis) Contribution of foregrounds

Non-Gaussianity and topological defects LCDM Strings

= ? + Why Gaussianity of signal is important ? What else ? Power spectrum: = ? +

Phase analysis and non-Gaussianity

Phase analysis

It is phase k that keep Max’s face, not amplitude |k| !! transformed Planck Planck satellite and transformed Planck have the same power spectrum (same |k| ), they have different “faces” due to different phases: It is phase k that keep Max’s face, not amplitude |k| !! Planck satellite Max Planck |k| exp(ik) FT-1[ ] |k| exp(ik) |k| exp(ik)

Gaussian Random Fields Strict definition of Gaussianity: They possess Fourier modes whose real and imaginary parts are independently distributed and both Gaussian, Weak definition of Gaussianity : random phase hypothesis the Fourier phases are uniformly random between 0 and (by Central Limit Theorem)

Non-Gaussianity: phase diagram

Non-Gaussian map, l=350-352 Gaussian map, l=350-352

Circular statistics of phases (Fisher 1993)

Phase cross-correlation between WMAP CMB signal and foregrounds. P Phase cross-correlation between WMAP CMB signal and foregrounds. P.Naselsky, A.Doroshkevich and O.Verkhodanov, 2003,ApJ.Lett,599,53 P.Naselsky, A.Doroshkevich , O.Verkhodanov, 2004,MNRAS,347,795

Multipole expansion L = 2 (quadrupole) L =3 (octupole) L = 5 L = 4

Quadrupole and component separation

Asymmetry of the WMAP signal

Quadrupole phase diagram (Naselsky, Verkhodanov,2006) Red ILC (III) Black Foreground Solid (l,m)=(2,1) Dashed (l,m)=(2,2) Red: ILC(III) Black Solid: Dipole Cosmological Black Dash: Dipole non-Cosmo

What is ILC map ? Obtained from 5 channels by minimization of correlation with foregrounds

Distribution of correlation coefficients (Naselsky, Verkhodanov,2007, not published ) 10000 simulations of L=2 maps (by Eriksen et al., 2003) Simulated input maps ILC maps

The mode=0 (C ) defines correlations 20 ILC C20 initial ILC C20 corrected

Some tricks when find same phases Even (l+m) harmonics V channel Odd (l+m) harmonics ILC map

V channel, odd (l+m) ILC

V channel, odd (l+m) V channel, odd (l+m) ILC ILC

Non-Gaussianity of the WMAP It's time to think and to work hard !

Binning

|aℓm| |aℓmCMB| |aℓm| The importance of phases: morphology and phases exp(iℓm) |aℓmCMB| exp(iℓmCMB)  |aℓm| exp(iℓmCMB)