Collaborators within DK-Planck
community
Andrei Doroshkevich
(TAC,ASC FIRAN)
Per Rex
H..U Norgaard Christensen (NBI)
Igor D. Novikov ( NBI)
-Nielsen, DSRC
Oleg V. Verhodanov
(TAC,SAO RAN)
Pavel D. Naselsky ( NBI)
Lung-Yih Chiang (NBI)
Why the issue of
Non-Gaussianity
is important for
Non-Gaussianity
of
the
development
CMB
sky
of cosmology ?
P.Naselsky
NBI, the PLANCK scientist
“BIG BANG”
Ω≈1 n≈0.97
Non-linear development
Gaussianity!!
²/2σ²)dδ
of the quantum P(δ)dδ~exp(-δ
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 the
Quantum fluctuations from
Inflation in radio waves
Definition of the power spectra

ΔT(θ,φ)  

| a
m
| e xp(i m )Ym(θ, φ)
  0 m  
C  ( m ,  bar ,   , n,......) 
Gaussian or
non-Gaussian
1
2
|
a
(

,

,

,
n
,......)
|

m
m
bar

2  1 m
C  / C   1 / f (   1 / 2 )
Gaussian only !
Cosmology before WMAP
The temperature anisotropy and temperature
polarization cross power spectrum
Precision
cosmology !!!
BOOMERANG,
MAXIMA-1,CBI,ARCHEOPS,VSA,DASI,
WMAP
+……. SN1a,
2dF,He, D
BIMA +……. SN1a, 2dF,He,D…
CMB
Ωbh2 =0.02 !
WHY
Cosmology of
NOT FOR
the XX century US ?
Cosmology of the XXI century
Important question is WHY?
Dark matter density
Dark energy density
≈1/3
1/π ? (D=3)/(D=10) ?
Topology ?
What about
Baryonic matter density
Dark matter density
Extra dimensions ?
? Baryosynthesis?
Dark energy
Development of
Cosmology and
High energy physics
}
Dark matter
Φ(x, t)=Ψ(x, t)*
exp [iΛ(x, t)] Baryonic matter
S.Bonometto et al,2004,2005
Non linear theory of dark energy-dark matter
coupling
•Link between adiabatic and isocurvature perturbations
•Weak Non-Gaussianity of the CMB
Reionization of the cosmic
plasma by the first quasars,
galaxies, and stars
Reionization
300 Mpc
3Mpc
WMAP
PLANCK,
2007
Two news from the WMAP data analysis
1.The CMB signal is
Gaussian !
Komatsu et al, 2003 (WMAP team )
2. The CMB signal is
non- Gaussian
WMAP map: Gaussian by WMAP
science team with 95% CL
|f |<100
f    f **
,
Non-Gaussianity is not a dog!”
Ya.B.Zel’dovich
f*ΔΦΔΦ
The definition of Gaussianity
( T < T  )
P( T)dT  N e xp[
]dT
2
2
2
am | am | exp(im)
Methods of detection of Non-Gaussianity in the WMAP sky
Image domain
1.Peak statistics
2. Minkowski functionals
Multipoles domain
1.Phases analysis
(trigonometric moments of
phases, phase cross-correlations,
Pearson’s random walk statistic,
3. Wavelets
4.Curvature distribution
2.Minkowski vectors
5.Non-uniformity of the
power spectra distribution
over patches of the sky
3. Cooper's statistic for phases
6.Skiwness and kurtosis
7. Bispectrum
…………….
WMAP signal
is Non-Gaussian
FOREGROUNS +
instrumental noise+
systematic effects
CMB maps derived from the WMAP data
NOT FOR
ILC
INVESTIGAl<100
TION OF THE
CMB !!!??
ErFM
l<512
FCM
l<512
WFM
l<512
Image analysis for non-Gaussianity test
Pixel by pixel
Foregrounds ?
FCM-ErFCM
ILC-WFM
ILC-ErFCM
V band l=400
WMAP KP masks
Asymmetry of the CMB
power
*South-north asymmetry of the
COBE and the WMAP signals.
NEP
SEP
Global anisotropy
of the Universe.
NEP
SEP
WHY ?
Non-CMB tools
FCM
WFCM
Q-W
V-W
FCM-WFCM
MV
NON-CMB
L<512
L<100
L<30
Alignment of the low multipoles
Schwarz et al,2004
Gaussian Random Fields
Strict definition of Gaussianity:
am | am | exp(ilm )  [am ]  im[am ]
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 2p
(by Central Limit Theorem)
Planck satellite
|dk| exp(ik)
transformed Planck
FT-1[ |dk|exp(ik)]
Max Planck
|dk| exp(ik)
Planck satellite and transformed Planck have the same
power spectrum (same |dk| ), they have different “faces”
due to different phases:
It is phase k that keep Max’s face, not amplitude |dk| !!
Asymmetry of the WMAP
phases
S i( l )
   tan {
}
C s( l )
1
S i( l ) 
C s( l ) 

1

 si n (
lm
  l   ,m )
m 1

1

 cos(
m 1
lm
  l   ,m )
Foreground-cleaned map
Foreground-cleaned map
ℓ
m
Asymmetry of the WMAP
phases
ILC
TOH
WTOH
L-1,L+1 correlation
through m- direction
M-1,M correlation
through - L direction
NO Evidence of Primordial Magnetic Field !
Naselsky, Verkhodanov, Novikov,Olesen,Chiang,ApJ,2004
Non-Gaussianity of the WMAP.
WHY ?
NON-GAUSSIANITY
Primordial
(Inflation ?)
Foregrounds + systematic
f    f **
NEW
PHYSICS
S= G + NG
Summary 2003-2005
1.Residues of the foregrounds separation
Chiang ,Naselsky, Verkhodanov and Way,ApJ.Lett2003;
Naselsky , Doroshkevich and Verkhodanov,ApJ.Lett,2003;
Naselsky , Doroshkevich and Verkhodanov,MNRAS,2004;
Park, MNRAS,2004;
Eriksen, D.Novikov, Lille,Gorski, ApJ,2004 ;
Naselsky, Verkhodanov, Novikov,Olesen,Chiang,ApJ,2004,…
2. Systematic effects
Hansen, Vittorio,ApJ.Lett.2004 (+)
Vielva et al,MNRAS, 2004 (-)
3. Primordial
Bershadskii, Skrinevasan, Phys.Lett.,2003;2004 (magnetic field)
Vielva et al,MNRAS, 2004
Hansen, Bandy, Gorski,MNRAS,2004
Wandelt ,ApJ.Lett,2004
Non-Gaussianity is not a dog!”
Ya.B.Zel’dovich
Sorry!