CMB as a physics laboratory. Recombination Hydrogen is neutralHydrogen is ionized Thomson Scattering T = 0.3 eV

CMB as a physics CMB as a physics laboratorylaboratory

RecombinatioRecombinationn

Hydrogen is neutralHydrogen is ionized

Thomson Scattering

T = 0.3 eV << me c2

CosmicCosmic

Tegmark, 2000

Dust

Point sources

Free freeSynchrot.

MicrowaveMicrowaveDecoupling: photon mean free path, ne

Tdec=3000K depends essentially only on the baryon density (ne) and on the total matter density (H-1 ).

After 10Gyr, this has to cool by a factor of roughly 1000: the present black body spectrum at Tcmb=2.726K is then an immediate indication that the values of totb H0 we currently use are in the right ballpark.

BackgroundBackground

CMBz = 1100

HistoryHistory19411941 McKellarMcKellar

CH,CN excitation CH,CN excitation

temperature in starstemperature in stars

19491949 GamowGamow

Prediction TcmbPrediction Tcmb

19641964 Penzias WilsonPenzias Wilson 1010-1-1

19661966 Sachs WolfeSachs Wolfe

DT/T grav.DT/T grav.

19701970 Peebles YuPeebles Yu

DT/T ThomsonDT/T Thomson

19921992 COBECOBE 1010-4-4 7700

19991999 BoomerangBoomerang 1010-5-5 2020’’

20022002 DASIDASI

PolarizationPolarization

20032003 WMapWMap 1010-5-5 1818’’

20072007 PlanckPlanck 1010-6-6 77’’

Is the Universe….Is the Universe….

Open, closed, flat, compact,Open, closed, flat, compact,

accelerated, deceleratedaccelerated, decelerated, ,

initially gaussian, scale invariant,initially gaussian, scale invariant,

adiabatic, isocurvature,adiabatic, isocurvature,

einsteinianeinsteinian…?…?

• GeometryGeometry• DynamicsDynamics• Initial conditionsInitial conditions• Growth of Growth of

fluctuationsfluctuations

Ask the CMB….Ask the CMB….

What do we expect to find What do we expect to find on the CMB?on the CMB?

• oo , ,bb ,n ,n R,NR R,NR ,H,H00

• nnss, n, nt t , ,

• inflation pot. V (inflation pot. V ()) ww· VEPVEP• topological defectstopological defects• bouncing universebouncing universe• Compact topologyCompact topology• Extra dimensionsExtra dimensions

the standard universe

the unexpected universe

the weird universe

XXXXXboring

XXXXXXXexciting

very exciting XXXX

Perturbing the CMBPerturbing the CMB• Observable: radiation intensity per unit frequency per Observable: radiation intensity per unit frequency per

polarization state at each point in sky:polarization state at each point in sky:

P, P, EE• In a homogeneous universe, the CMB is the same perfect In a homogeneous universe, the CMB is the same perfect

black-body in every directionblack-body in every direction

• In a inhomogenous universe, the CMB can vary in:In a inhomogenous universe, the CMB can vary in:

intensityintensity Grav. Pot, Doppler, intrinsic Grav. Pot, Doppler, intrinsic fluctuationsfluctuations

polarizatiopolarizationn

anisotropic scattering, anisotropic scattering, grav. wavesgrav. waves

PP

spectrumspectrum energy injection z<10energy injection z<1066 EE

Predicting the CMBPredicting the CMB

• General relativistic equations for baryons, dark General relativistic equations for baryons, dark matter, radiation, neutrinos,...matter, radiation, neutrinos,...

• Solve the perturbed, relativistic, coupled, Solve the perturbed, relativistic, coupled, Boltzmann equationBoltzmann equation

• Obtain the DT/T for all Fourier modes and at all Obtain the DT/T for all Fourier modes and at all timestimes

• Convert to the DT/T on a sphere at z=1100 Convert to the DT/T on a sphere at z=1100 around the observeraround the observer

Complicate but linear !

Fluctuation spectrumFluctuation spectrum

From DT/T To Cl

Largescales

Smallscales

Temperature fluctuationsTemperature fluctuations

ArchaicArchaic

(>horizon (>horizon scale)scale)

Middle AgeMiddle Age ContemporaryContemporary

(<damping (<damping scale)scale)

> 2> 200

l l < 100< 100 220 0 < < <10’ <10’

100 < 100 < l l < < 10001000

< 10’< 10’

l l > 1000> 1000

zz>>1000>>1000 1000>1000>zz>1>100

zz<10<10

Archaic CMBArchaic CMB

• Sachs-Wolfe effect of Sachs-Wolfe effect of superhorizonsuperhorizon inflationary perturbationsinflationary perturbations

• Integrated Sachs-Wolfe effect of Integrated Sachs-Wolfe effect of subhorizonsubhorizon fluctuations: when the fluctuations: when the gravitational potential is not constant gravitational potential is not constant (eg, nonflat metric, other components, (eg, nonflat metric, other components, non-linearity, etc)non-linearity, etc)

Sachs-Wolfe effectSachs-Wolfe effect

Last Scatt. Surface

ISW

SW

z = 1100

z = 0

.

Fluctuation spectrumFluctuation spectrum

22)(

),(),(

),(),(

expansionharmonicSpherical

mm

mm

mmm

T

TaC

dYT

Ta

YaT

T

Sachs-Wolfe effectSachs-Wolfe effect

Data: Cobe +Boomerang

P(k)=Akn

)1(4

)()(

ZeldovichHarrison

)()()(),(

:Spectrum

)()(2

3)()(4

:spacek in Poisson3

WolfeSach

40

2

22242

2222

AHC

AkakP

kjadkaHdkkGT

TC

aaaHaaak

T

T

s

SW

k

dkmok

SW

kmok

Integrated Sachs-Wolfe Integrated Sachs-Wolfe effecteffect

))()(()(

),(

:

22224

2

aaadt

dkdtjdkH

dtT

T

dt

dkGdkC

Spectrum

kmo

k

ISW

Middle age CMBMiddle age CMB

• Acoustic perturbations:Acoustic perturbations:• perturbations oscillate acoustically perturbations oscillate acoustically

when their size is smaller than the when their size is smaller than the soundsound horizonhorizon (the pressure wave (the pressure wave has the time to cross the has the time to cross the structure)structure)

• The oscillations are The oscillations are coherent !coherent !

The sound horizon at The sound horizon at decouplingdecoupling

•The decoupling occurred 300,000 yrs after the big bang•Acoustic perturbations in the photon-baryon plasma travelled at the sound speed

Therefore they propagated for

(almost) independently of cosmology.

3/ccs

Mpclyr 05.0000,170

Acoustic oscillationsAcoustic oscillations

LSS

z = 1100

z = 0

Coupled fluctuationsCoupled fluctuations

D. Eisenstein

Acoustic oscillationsAcoustic oscillations

First peak: Sound horizonFirst peak: Sound horizon

• angular size : sensitive to the angular size : sensitive to the dominantdominant components components

• amplitude : sensitive to the amplitude : sensitive to the baryonbaryon componentcomponent

Sound Sound horizonhorizon

SHSH

D

SHSH

zs

kk

kk

z

R

R

zE

dzcSH

kx

kx

kx

xS

zEHHzE

dzcSH

kr

drtadtc

dsFRW

d

d

deg1

)(r

horizon sound

1)sinh(

0

1)sin(

)(

)(,)(

r

distance1

)(

0

10SH

2/12/1

2/12/1

00

10D

2

2222

2

SH

DR

SHR

Acoustic peaksAcoustic peaks

Data: Boomerang 1999

Contemporary CMBContemporary CMB

• Processes along the line-of-sight:Processes along the line-of-sight:• SZ effect: inverse Compton SZ effect: inverse Compton

scattering (scattering (cluster massescluster masses))• stochastic lensing (stochastic lensing ( mass mass

fluctuation powerfluctuation power))• reionization (reionization ( epoch of first lightepoch of first light))

Temperature field Lensed temperature field

Weak Lensing in CMB

Hu 2002

How is polarization How is polarization generated? generated?

Thomson Scattering

GravityWaves

Density pert. &

Gravity Waves

CMBCMBin in 1999…1999…

……20012001

……20032003

SensitivitySensitivity Hu, 2002

Now

Map, 2003

Planck, 2007

The geometric effectThe geometric effect

The kinematic effectThe kinematic effect

)'(

')(

zH

dzzr