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![Page 1: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/1.jpg)
Cosmic Microwave Background
Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications
for Cosmology
Carlo Baccigalupi, March 31, 2004
![Page 2: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/2.jpg)
Outline…Outline…• Present: angular powerPresent: angular power• Future: ImagingFuture: Imaging• CMB cleaningCMB cleaning• Primordial non-GaussianityPrimordial non-Gaussianity• ReionizationReionization• LensingLensing• ……
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The Present CMB: Measuring Angular Power
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Before And After The First Light
![Page 5: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/5.jpg)
From COBE to WMAP
Courtesy of the NASA/WMAP Science Team
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WMAP Maps
23 GHz, 0.82o , 6 mK/Nobs
33 GHz, 0.62o , 3 mK/Nobs
41 GHz, 0.49o , 2 mK/Nobs
61 GHz, 0.33o ,
1.4 mK/Nobs
94 GHz, 0.21o ,
1.4 mK/Nobs
Nobs ' 103
Courtesy of the NASA/WMAP Science Team
![Page 7: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/7.jpg)
The CMB Angular Power Spctrum
![Page 8: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/8.jpg)
Throwing Pebbles In The Primordial Pond
Homogeneity& Isotropy
Black Body Spectrum
+
+
+
Courtesy of the NASA/WMAP Science Team
![Page 9: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/9.jpg)
The Sound Of The Early Universe
Isocurvature
Adiabatic
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![Page 12: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/12.jpg)
+
![Page 13: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/13.jpg)
The Window On The Early Universe
T/T// 0 on all scales
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Cosmological Parameters
Basic Analysis: h, ns, k ¢ dns/dk, b h2, m h2, A,
WMAP, WMAP+ACBAR+CBI+2dF+LymanExtension: , m ,wDE, r
h=0.71§ 0.06, 0.71+0.04
ns=0.91§ 0.06, 0.93§ 0.03k ¢ dns/dk =..., -0.031
+0.016-0.017
b h2 =0.022§ 0.001, 0.0224 § 0.0009m h2 =0.14§ 0.01, 0.135
+0.008-0.009
A=0.9 § 0.1, 0.83+0.09-0.08
-0.03
=0.20§ 0.07, 0.17 § 0.06
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Extension: WMAP+ACBAR+CBI+HST+SNIa+(H0>50 km/sec/Mpc):
=1.02 § 0.02Extension: m
Extension: wDE
Extension: r
WMAP+ACBAR+CBI+2dF:
h2=imi/93.5 eV < 0.0076 ´ m <0.23 eV
WMAP+ACBAR+CBI+HST+SNIa+2dF:
wDE < -0.78
WMAP+ACBAR+CBI+2dF+infl.cons.rel.:
r < -0.71
![Page 16: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/16.jpg)
Reionisation
ClT/ exp(-2) on l > lrh
ClT,TE,E,B boosted on l < lrh
' 0.12
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The Future CMB: Imaging
Cosmology
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CMB Spectrum…
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CMB Spectrum…
Reionization: Non-Gaussian Lensing: Non-GaussianPrimordial GWs
Primordial Density Perts.: non-Gaussian?
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CMB Spectrum…
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Planck According To Dodelson & Hu 2003
![Page 22: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/22.jpg)
True CMB…
![Page 23: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/23.jpg)
WMAP CMB…
![Page 24: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/24.jpg)
True CMB…
![Page 25: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/25.jpg)
Planck CMB…
![Page 26: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/26.jpg)
True CMB…
![Page 27: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/27.jpg)
CMBpol CMB…
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CMB CMB CorruptedCorrupted
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The Future CMB:
Foreground Removal
![Page 30: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/30.jpg)
CMB CMB CorruptedCorrupted
![Page 31: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/31.jpg)
Fast Independent Component Fast Independent Component Analysis (FastICA)Analysis (FastICA)
x=As+nx=As+n, find W such that, find W such that Wx=s+WnWx=s+Wn FastICA main loop: construct FastICA main loop: construct
W W row by rowrow by rowChoose Choose initial initial wwUpdate Update throughthrough
wwnewnew=E[xg(w=E[xg(wTTx)]-x)]-wE(g’(wwE(g’(wTTx))x))Compare with Compare with ww. If not . If not
converged go back; if converged go back; if converged start up next converged start up next row, keeping orthogonalityrow, keeping orthogonality
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OUT
IN
FastICA on Planck SimulationsFastICA on Planck SimulationsMaino et al. 2002Maino et al. 2002
Planck nominal Planck nominal performanceperformance
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See Baccigalupi et al. 2003 for results with See Baccigalupi et al. 2003 for results with Planck nominal performancePlanck nominal performance
Component Separation in Component Separation in PolarisationPolarisation
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• Perform Monte Carlo simulations to Perform Monte Carlo simulations to quantify the effect of noise distribution quantify the effect of noise distribution
• Build Criteria to Identify Physical Build Criteria to Identify Physical Components in a Heavy Noise EnviromentComponents in a Heavy Noise Enviroment
• Add priors to check quality and consistency Add priors to check quality and consistency of the resultsof the results
• Extract Cosmological Parameters and Extract Cosmological Parameters and Foreground ScienceForeground Science
FastICA and FastICA and COBECOBE
Maino et al. Maino et al. 20032003
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FastICA & COBE FastICA & COBE Maino et al. 2003Maino et al. 2003
BlinBlindd
Non-Non-BlindBlind
![Page 36: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/36.jpg)
The Future CMB: Imaging
Physical Cosmology
![Page 37: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/37.jpg)
Primordial non-Primordial non-GaussianityGaussianity
Liguori et al. 2003Liguori et al. 2003
=L+fNL(L2-<L
2>)
The simplest inflationary scenario predicts fNL' 10-1
WMAP: -58< fNL< -134
Planck forecast in progress
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Imaging Reionization…Imaging Reionization…
9.5 arcminutes
T/T
Salvaterra, Ferrara et al. 2004 in prep.Salvaterra, Ferrara et al. 2004 in prep.
Normal Stars in proto-galaxiesNormal Stars in proto-galaxies
20% escape fraction20% escape fraction
CMB scattering on moving electornsCMB scattering on moving electorns
compatible with WMAP compatible with WMAP
![Page 39: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/39.jpg)
Dark Energy & CMB: beyond CDark Energy & CMB: beyond Cl l s s
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
![Page 40: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/40.jpg)
CMB bispectrum CMB bispectrum
BBllm m
l`l`m`m`
l``l``m``m``=a=almlm a al`m`l`m` a al``m``l``m``
aalmlm==ss ( ( )Y )Ylmlm(( )d )d
BBl l`l``l l`l``==m m` m``m m` m`` ( (mmllm`m`
l`l`m``m``
l``l``) a) almlm a al`m`l`m` a al``m``l``m``
ll
l`l`l``l``
(( ) ) ´́ T(T( )/T )/T
![Page 41: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/41.jpg)
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >=0>=0
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >> 0 0
![Page 42: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/42.jpg)
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
<B<Bl l`l``l l`l``>=[(2l+1)(2l`+1)(2l``+1)/16>=[(2l+1)(2l`+1)(2l``+1)/16]]1/21/2((00ll00
l`l`0``0``
l``l``) ) ¢¢
¢ ¢ [l(l+1)- l`(l`+1)+ l``(l``+1) ][l(l+1)- l`(l`+1)+ l``(l``+1) ] CCl l Q(l``)Q(l``) +Perm.+Perm.
Q(l)=Q(l)=ss00dec dec D(z) F(z) D(z) F(z)
dzdz
D(z)=[r(zD(z)=[r(zdecdec)-r(z)]/r(z)-r(z)]/r(zdecdec)r(z))r(z)33
F(z)=dPF(z)=dP/dz|/dz|k=l/r(z)k=l/r(z)
PP=(3=(3m0 m0 /2)/2)22(H(H00/ck)/ck)44P(k,z)(1+z)P(k,z)(1+z)22 P(k,z)=AkP(k,z)=AknnT(k,z)T(k,z)22
(( ) = ) =lsslss((++)+)+ISW ISW '' lsslss(()+)+rrlsslss(())¢¢
ISWISW(( )=2 )=2ss00decdecdr ddr d (r, (r, )/d )/d
=2=2ss00decdecdr[(r-rdr[(r-rdecdec)/r)/rdecdecr]r]r,r,))
Hu & White 1997, Bartelmann & Schneider 2001, Hu & White 1997, Bartelmann & Schneider 2001, Komatsu & Spergel 2001, Verde & Spergel 2002Komatsu & Spergel 2001, Verde & Spergel 2002
![Page 43: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/43.jpg)
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
ll-1-1
=2=2 /k=r(z /k=r(z33)/l)/l
=r(z=r(z22)/l)/l
=r(z=r(z11)/l)/l
r(zr(z11))
r(zr(z22))
r(zr(z33))
zz11
zz22
zz33
zzrr
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CMB bispectrum line of sight chronology CMB bispectrum line of sight chronology
ll-1-1
horizon crossing, horizon crossing, decaying linearly, dQ/dz>0 decaying linearly, dQ/dz>0
zz!1!1 :super-horizon scales in a flat :super-horizon scales in a flat CDM universe, dPCDM universe, dP/d/d =0, dQ/dz =0, dQ/dz!! 0 0
zzrr
Non-linearity, Non-linearity, grows, dQ/dz<0 grows, dQ/dz<0
zz!! 0, 0, vanishes, dQ/dz vanishes, dQ/dz!! 0 0
onset of acceleration, change in cosmic onset of acceleration, change in cosmic equation of state, equation of state, decaying linearly, dQ/dz>0 decaying linearly, dQ/dz>0
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CMB bispectrum line of sight distributionCMB bispectrum line of sight distribution
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
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CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy Quintessence reference modelsQuintessence reference models
SUGRASUGRA
RPRP
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CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
Ma et al. Ma et al. 1999, 1999,
Smith et Smith et al. 2003al. 2003
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CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
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CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
![Page 50: Cosmic Microwave Background Acoustic Oscillations, Angular Power Spectrum, Imaging and Implications for Cosmology Carlo Baccigalupi, March 31, 2004.](https://reader035.fdocuments.in/reader035/viewer/2022062518/56649f575503460f94c7cc9b/html5/thumbnails/50.jpg)
CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
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CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >=0>=0
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >> 0 0
Giovi, Liguori et al. 2004, in preparation Giovi, Liguori et al. 2004, in preparation
=2=2ss00decdecdr[(r-rdr[(r-rdecdec)/r)/rdecdecr]r]r,r,))
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Continua…Continua…• Component Separation & WMAP…Component Separation & WMAP…• Impact of CMB bispectrum on Planck Impact of CMB bispectrum on Planck
Cosmological Parameter Estimation…Cosmological Parameter Estimation…• Weakly Lensed CMB Templates, Semi-Weakly Lensed CMB Templates, Semi-
analytical…analytical…• Weakly Lensed CMB Templates, Numerical…Weakly Lensed CMB Templates, Numerical…• Weakly Lensed CMB Templates, Weakly Lensed CMB Templates,
Polarisation…Polarisation…• Weakly Lensed CMB Templates, Comparison Weakly Lensed CMB Templates, Comparison
with Gravitational Wave Signal…with Gravitational Wave Signal…