Collaborators within Collaborators within DK-DK-PlanckPlanck communitycommunity
Lung-Yih Chiang (NBI)Lung-Yih Chiang (NBI)
Andrei Doroshkevich (TAC,ASC FIRAN)
Per Rex Christensen (NBI)
Igor D. Novikov ( NBI)
Pavel D. Naselsky ( NBI)
Oleg V. Verhodanov(TAC,SAO RAN)
H..U Norgaard-Nielsen, DSRC
Non-Gaussianity of the CMB sky
P.NaselskyNBI, the PLANCK scientist
Why the issue of Why the issue of Non-Gaussianity Non-Gaussianity is important for is important for developmentdevelopmentof cosmology ?of cosmology ?
“BIG BANG”
Ω≈1 n≈0.97Gaussianity!!P(δ)dδ~exp(-δ ²/2σ²)dδ
Non-linear development of the quantum fluctuation
Non-Gaussianity!!
Transition from primordial (Gaussian) fluctuations to non-linear structures (galaxies , clusters and LSS ) change statistical properties of the adiabatic perturbations.
Picture of thePicture of theQuantum fluctuations fromQuantum fluctuations fromInflation in Inflation in radio wavesradio waves
Definition of the power spectraDefinition of the power spectra
)φ,(θY)iexp(|a|ΔT(θ,φ)
0 mmmm
2barm
mm
barm
|,......)n,,,(a|12
1
,......)n,,,(C
)2/1(f/1C/C
Gaussian or non-Gaussian
Gaussian only !
Cosmology before WMAP
The temperature anisotropy and temperature The temperature anisotropy and temperature
polarization cross power spectrumpolarization cross power spectrum
Precision cosmology !!!
BOOMERANG, MAXIMA-1,CBI,ARCHEOPS,VSA,DASI,BIMA +……. SN1a, 2dF,He,D…
CMB
Ω h =0.02 !b2
WMAP +……. SN1a, 2dF,He, D
WHY NOT FORNOT FORUS ?US ?
CosmologyCosmology ofof the XX centurythe XX century
Important question is WHY?Important question is WHY?
Dark matter densityDark energy density ≈1/3 1/π ? (D=3)/(D=10) ?
What about What about
ExtraExtra dimensions ?dimensions ?Topology ?Topology ?
Baryonic matter density Dark matter density ?Baryosynthesis?
CosmologyCosmology of the XXI centuryof the XXI century
Development of Development of Cosmology andCosmology andHigh energy physicsHigh energy physics
Dark energyDark energy
Dark matterDark matter
Baryonic matterBaryonic matter
}
ΦΦ(x, t)=(x, t)=ΨΨ(x, t)*(x, t)* exp [iexp [iΛΛ(x, t)](x, t)]
S.Bonometto et al,2004,2005
Non linear theory of dark energy-dark matterNon linear theory of dark energy-dark matter couplingcoupling
•Link between adiabatic and isocurvature perturbations•Weak Non-Gaussianity of the CMB
Reionization of the cosmic Reionization of the cosmic plasma by the first quasars, plasma by the first quasars, galaxies, and starsgalaxies, and stars
300 Mpc
3Mpc
ReionizationReionization
WMAPWMAP
PLANCK,PLANCK,20072007
Two news from the WMAP data analysisTwo news from the WMAP data analysis
1.The CMB signal is The CMB signal is Gaussian !Gaussian !
Komatsu et al, 2003 (WMAP teamteam ) )
2. The CMB signal is2. The CMB signal is non- Gaussiannon- Gaussian
WMAPWMAP map: Gaussian by map: Gaussian by WMAPWMAP science team with 95% CLscience team with 95% CL
f
f
, Non-Gaussianity is not a dog!” Non-Gaussianity is not a dog!” Ya.B.Zel’dovichYa.B.Zel’dovich
f*ΔΔΦΦΔΔΦΦ
The definition of Gaussianity
)iexp(|a|a mmm
dT]2
)TT(exp[NdT)T(P
2
2
Methods of detection of Non-Gaussianity in the WMAP sky
Image domain Multipoles domain
1.Peak statistics
2. Minkowski functionals
3. Wavelets
4.Curvature distribution
5.Non-uniformity of thepower spectra distributionover patches of the sky
6.Skiwness and kurtosis
7. Bispectrum
…………….
1.Phases analysis(trigonometric moments of phases, phase cross-correlations,Pearson’s random walk statistic,
2.Minkowski vectors
3. Cooper's statistic for phases
WMAP signalWMAP signal is Non-Gaussianis Non-Gaussian
FOREGROUNS +FOREGROUNS +instrumental noise+instrumental noise+systematic effectssystematic effects
CMB maps derived from the WMAP data
ILCl<100
FCM l<512
WFM l<512
ErFM l<512
NOT FORNOT FOR INVESTIGA-INVESTIGA-TION OF THETION OF THE CMB !!!??CMB !!!??
Image analysis for non-Gaussianity test
Pixel by pixel
Foregrounds ?
FCM-ErFCM ILC-ErFCM
ILC-WFM V band l=400
WMAP KP masksWMAP KP masks
Asymmetry of the CMB Asymmetry of the CMB powerpower
*South-north asymmetry of the *South-north asymmetry of the COBE and the WMAP signals.COBE and the WMAP signals.
Global anisotropy of the Universe.
NEP
NEP
SEP
SEP WHY ?
Non-CMB toolsNon-CMB toolsQ-W
V-W
FCM
WFCM
FCM-WFCM
MV
L<512
NON-CMB
L<100
L<30
Alignment of the low multipoles Schwarz et al,2004
Gaussian Random FieldsGaussian Random FieldsStrict 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)
]a[mi]a[)iexp(|a|a mmlmmm
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 FT-1[ ]|k| exp(ik) |k| exp(ik)|k|exp(ik)
Asymmetry of the WMAP Asymmetry of the WMAP phasesphases
)cos()l(Cs
)sin()l(Si
})l(Cs
)l(Si{tan
1mm,llm
1
1mm,llm
1
1
Foreground-cleaned map
Foreground-cleaned map
ℓ
m
Asymmetry of the WMAP Asymmetry of the WMAP phasesphases
L-1,L+1 correlation through m- direction
M-1,M correlationthrough - L direction
ILC
WTOH
TOH
NO Evidence of Primordial Magnetic Field !Naselsky, Verkhodanov, Novikov,Olesen,Chiang,ApJ,2004
Non-Gaussianity of the WMAP.Non-Gaussianity of the WMAP.
WHY ?
Primordial(Inflation ?)
Foregrounds + systematic
NON-GAUSSIANITY
NEWPHYSICS
S= G + NG
f
Summary 2003-2005Summary 2003-20051.Residues of the foregrounds separation1.Residues of the foregrounds separationChiang ,Naselsky, Verkhodanov and Way,ApJ.Lett2003; Chiang ,Naselsky, Verkhodanov and Way,ApJ.Lett2003; Naselsky , Doroshkevich and Verkhodanov,ApJ.Lett,2003;Naselsky , Doroshkevich and Verkhodanov,ApJ.Lett,2003;Naselsky , Doroshkevich and Verkhodanov,MNRAS,2004;Naselsky , Doroshkevich and Verkhodanov,MNRAS,2004;Park, MNRAS,2004;Park, MNRAS,2004;Eriksen, D.Novikov, Lille,Gorski, ApJ,2004 ;Eriksen, D.Novikov, Lille,Gorski, ApJ,2004 ;Naselsky, Verkhodanov, Novikov,Olesen,Chiang,ApJ,2004,…Naselsky, Verkhodanov, Novikov,Olesen,Chiang,ApJ,2004,…
2. Systematic effects2. Systematic effectsHansen, Vittorio,ApJ.Lett.2004 (+)Hansen, Vittorio,ApJ.Lett.2004 (+)Vielva et al,MNRAS, 2004 (-)Vielva et al,MNRAS, 2004 (-)
3. Primordial3. PrimordialBershadskii, Skrinevasan, Phys.Lett.,2003;2004 (magnetic field)Bershadskii, Skrinevasan, Phys.Lett.,2003;2004 (magnetic field)Vielva et al,MNRAS, 2004 Vielva et al,MNRAS, 2004 Hansen, Bandy, Gorski,MNRAS,2004Hansen, Bandy, Gorski,MNRAS,2004Wandelt ,ApJ.Lett,2004Wandelt ,ApJ.Lett,2004
Non-Gaussianity is not a dog!” Non-Gaussianity is not a dog!” Ya.B.Zel’dovichYa.B.Zel’dovich
Sorry!
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