The Physics of Cosmic Microwave Background Anisotropy

The Physics of

WMAP Cosmic Microwave Background Anisotropy Wayne Hu NAS Meeting Agra, India WMAP 3yr Data

WMAP 3yr: Spergel et al. 2006

5000 ) 2 4000 ( µ K

l

C 3000

2000 l ( +1)/2 π

1000

0 200 400 600 800 1000 l (multipole moment) In the Beginning...

Hu & White (2004); artist:B. Christie/SciAm; available at http://background.uchicago.edu Physical Landscape

IAB 100 Sask Viper TOCO 80 BAM Sound Waves RING 60 Baryon CAT QMAP LoadingMaxima MAX D T ( m K) SP MSAM Initial Ten Radiation 40 FIRS OVROATCA Conditions ARGOIAC DrivingSuZIE BOOM Dissipation WD BIMA BOOM 20 COBE Pyth

W. Hu 11/00 10 100 1000 l Power Spectra of Maps •Original

64º

•Band Filtered Acoustic Oscillations Gravitational Ringing •Gravitational potential wells •Fluid falls into wells, pressure resists: acoustic oscillations Seeing Sound •Oscillations frozen as neutral hydrogen forms •Compression=hot spots, Rarefaction=cold spots Extrema=Peaks •Harmonics: like sound in a cavity •Cavity: time (x sound speed = sound horizon)

Ionized Neutral Ionized Neutral Θ+Ψ First Θ+Ψ T /

T Peak ∆

time time sound k1=π/ horizon k2=2k1 Second Peak Peaks in Angular Power •The Anisotropy Formation Process

The First Peak Weighing with Geometry •Physical scale of peak = distance sound travels •Angular scale measured: flat universe at critical density of matter and energy

Flat

Closed Curvature in the Power Spectrum •Features scale with angular diameter distance •Angular location of the first peak The Second Peak Baryon & Inertia

•Baryons add inertia to the fluid

•= adding mass on a spring

•Unequal amplitudes Baryons in the Power Spectrum The Third Peak Radiation and Dark Matter •Radiation domination: potential wells created by CMB itself •Pressure support ⇒ potential decay •Elimination of modulation from baryon loading Dark Matter in the Power Spectrum Damping Tail Dissipation • Photons and baryons imperfectly coupled • Random walk with the Thomson mean free path • Dissipation of fluctuations upto diffusion length at recombination

Recombination Viscosity • Microphysically, dissipation from fluid viscosity • Quadrupole anisotropy in CMB

m=0 hot

v cold

hot v Time Evolution • Rise of quadrupole causes fall in temperature fluctuations

Ψ damping

quadrupole driving temperature 5 10 15 20 time ks/π Polarization Patterns Polarization from Thomson Scattering

• Differential cross section depends on polarization and angle

dσ 3 0 2 = |εˆ · εˆ| σT dΩ 8π dσ 3 0 2 = |εˆ · εˆ| σT dΩ 8π Polarization from Thomson Scattering

• Isotropic radiation scatters into unpolarized radiation Polarization from Thomson Scattering

• Quadrupole anisotropies scatter into linear polarization

aligned with cold lobe Whence Polarization Anisotropy? • Observed photons scatter into the line of sight • Polarization arises from the projection of the quadrupole on the transverse plane E-mode Polarization • Polarization points along the direction of plane wave or amplitude variation

E-tensor harmonic l=2, m=0 Polarized Landscape 100

10 reionization ΘE

1 EE

∆ ( µ K) BB

0.1 gravitational lensing gravitational waves 0.01 10 100 1000

Hu & Dodelson (2002) l (multipole) Gravitational Waves Gravitational Waves • Inflation predicts near scale invariant spectrum of gravitational waves • Amplitude proportional to the square of the Ei=V1/4 energy scale • If inflation is associated with the grand unification Ei~1016 GeV and potentially observable

transverse-traceless distortion Gravitational Wave Pattern • Projection of the quadrupole anisotropy gives polarization pattern • Transverse polarization of gravitational waves breaks azimuthal symmetry - B-modes

density gravitational perturbation wave Summary • Physics of CMB anisotropy is simple and well understood • Acoustic oscillations in plasma before recombination lead to peaks whose features determine matter-energy content of Universe • Thomson scattering of quadrupole anisotropy generates linear polarization whose pattern may reveal gravitational radiation • Gravitational radiation can determine the physics of origin of structure in Universe