Results from Three-Results from Three-Year WMAP Year WMAP

ObservationsObservations

Eiichiro Komatsu (UT Austin)Eiichiro Komatsu (UT Austin)TeV II Particle AstrophysicsTeV II Particle Astrophysics

August 29, 2006August 29, 2006

Why Care About WMAP?Why Care About WMAP?• WMAP observes CMB. This is a conference about “Te

V” particle astrophysics. Why care about CMB? – The present-day temperature of CMB is 2.725K, or 2.35 m

eV.– The temperature at decoupling (where the most of CMB is

coming from) was ~3000K, or 0.26 eV. – The temperature at matter-radiation equality was ~9000K,

or 0.8 eV. • CMB is a nuisance for many particle astrophysicists:

it attenuates cosmic-ray particles traveling through the universe. (GZK)

• Why am I here?

What Can CMB Offer?What Can CMB Offer?• Baryon-to-photon ratio in the universe

– Sound speed and inertia of baryon-photon fluid• Matter-to-radiation ratio in the universe

– Dark matter abundance– “Radiation” may include photons, neutrinos as well as any other relativi

stic components.• Angular diameter distance to decoupling surface

– Peak position in l space ~ (Sound horizon)/(Angular Diameter Distance) • Time dependence of gravitational potential

– Integrated Sachs-Wolfe Effect, Dark energy• Primordial power spectrum (Scalar+Tensor)

– Constraints on inflationary models• Optical depth

– Cosmic reionization

Full Sky Microwave MapFull Sky Microwave Map

COBE/FIRAS: T=2.725 K

Uniform, “Fossil” Light from the Big Bang

Cosmic Microwave Background Radiation

COBE/FIRAS, 1990COBE/FIRAS, 1990Perfect blackbody = Thermal equilibrium = Big Bang

COBE/DMR, 1992COBE/DMR, 1992

Gravity is STRONGER in cold spots: T/T~

The Wilkinson Microwave The Wilkinson Microwave Anisotropy ProbeAnisotropy Probe

• A microwave satellite working at L2• Five frequency bands

– K (22GHz), Ka (33GHz), Q (41GHz), V (61GHz), W (94GHz)

• The Key Feature: Differential Measurement– The technique inherited from COBE– 10 “Differencing Assemblies” (DAs)– K1, Ka1, Q1, Q2, V1, V2, W1, W2, W3, & W4, each consisting of

two radiometers that are sensitive to orthogonal linear polarization modes.

• Temperature anisotropy is measured by single difference.

• Polarization anisotropy is measured by double difference.

K band (22GHz)K band (22GHz)

Ka Band (33GHz)Ka Band (33GHz)

Q Band (41GHz)Q Band (41GHz)

V Band (61GHz)V Band (61GHz)

W Band (94GHz)W Band (94GHz)

The Angular Power SpectrumThe Angular Power Spectrum• CMB temperature anisotropy is very close to

Gaussian; thus, its spherical harmonic transform, alm, is also Gaussian.

• Since alm is Gaussian, the power spectrum:

completely specifies statistical properties of CMB.

*lmlml aaC

WMAP 3-yr Power SpectrumWMAP 3-yr Power Spectrum

Physics of CMB AnisotropyPhysics of CMB Anisotropy

• SOLVE GENERAL RELATIVISTIC BOLTZMANN SOLVE GENERAL RELATIVISTIC BOLTZMANN EQUATIONS TO THE FIRST ORDER IN EQUATIONS TO THE FIRST ORDER IN PERTURBATIONSPERTURBATIONS

Use temperature fluctuations, =T/T, instead of f:

Expand the Boltzmann equation to the first order in perturbations:

where

describes the Sachs-Wolfe effect: purely GR fluctuations.

For metric perturbations in the form of:

ds2 a2 1 h00 d 2 ij hij dx idx j the Sachs-Wolfe terms are given by

where is the directional cosine of photon propagations.

Newtonian potential Curvature perturbations

1. The 1st term = gravitational redshift

2. The 2nd term = integrated Sachs-Wolfe effect

h00/2

hij/2

(higher T)

• When coupling is strong, photons and baryons move together and behave as a perfect fluid.

• When coupling becomes less strong, the photon-baryon fluid acquires shear viscosity.

• So, the problem can be formulated as “hydrodynamics”. (c.f. The Sachs-Wolfe effect was pure GR.)

Small-scale Anisotropy (<2 deg)Small-scale Anisotropy (<2 deg)

Collision term describing coupling between photons and baryons via electron scattering.

Boltzmann Equation to HydrodBoltzmann Equation to Hydrodynamicsynamics

Monopole: Energy density

Dipole: Velocity

Quadrupole: Stress

• Multipole expansion

• Energy density, Velocity, Stress

Photon Transport EquationsPhoton Transport Equations

f2=9/10 (no polarization), 3/4 (with polarization)

A = -h00/2, H = hii/2

C=Thomson scattering optical depth

CONTINUITY

EULER

Photon-baryon coupling

Baryon TransportBaryon Transport

Cold Dark Matter

The Strong Coupling RegimeThe Strong Coupling Regime

SOUND WAVE!

The Wave Form Tells Us The Wave Form Tells Us Cosmological ParametersCosmological Parameters

Higher baryon density

Lower sound speed

Compress more

Higher peaks at compression phase (even peaks)

What CMB MeasuresWhat CMB MeasuresA

mpl

itud

e of

tem

pera

ture

flu

ctua

tion

s at

a g

iven

sca

le, l

400 80020040 10010Multipole moment l~ Small scalesLarge scales

Ang.Diam. Distance

Baryon-to-photon Ratio

Mat-to-Radiation Ratio

ISW

CMB to ParametersCMB to Parameters

Measuring Matter-Radiation RatioMeasuring Matter-Radiation Ratio

where is the directional cosine of photon propagations.

1. The 1st term = gravitational redshift

2. The 2nd term = integrated Sachs-Wolfe effect

h00/2

hij/2

(higher T)

During the radiation dominated epoch, even CDM fluctuations cannot grow (the expansion of the Universe is too fast); thus, dark matter potential gets shallower and shallower as the Universe expands --> potential decay --> ISW --> Boost Cl.

Matter-Radiation RatioMatter-Radiation Ratio

• More extra radiation component means that the equality happens later.• Since gravitational potential decays during the radiation era (free-fall

time scale is longer than the expansion time scale during the radiation era), ISW effect increases anisotropy at around the Horizon size at the equality.

How Many (Effective) Neutrinos?How Many (Effective) Neutrinos?

So, It’s Been Three Years Since So, It’s Been Three Years Since The First Data Release. What Is The First Data Release. What Is

New Now?New Now?

POLARIZATION DATA!!POLARIZATION DATA!!

K Band (23 GHz)K Band (23 GHz)Dominated by synchrotron; Note that polarization direction is perpendicular to the magnetic field lines.

Ka Band (33 GHz)Ka Band (33 GHz)Synchrotron decreases as -3.2 from K to Ka band.

Q Band (41 GHz)Q Band (41 GHz)We still see significant polarized synchrotron in Q.

V Band (61 GHz)V Band (61 GHz)The polarized foreground emission is also smallest in V band. We can also see that noise is larger on the ecliptic plane.

W Band (94 GHz)W Band (94 GHz)While synchrotron is the smallest in W, polarized dust (hard to see by eyes) may contaminate in W band more than in V band.

Polarized Light Filtered

Polarized Light Un-filtered

Jargon: E-mode and B-modeJargon: E-mode and B-mode• Polarization is a rank-2 tensor field.• One can decompose it into a divergence-like

“E-mode” and a vorticity-like “B-mode”.

E-mode B-mode

Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky, Stebbins (1997)

Physics of CMB PolarizationPhysics of CMB Polarization• Thomson scattering generates polarization, if…

– Temperature quadrupole exists around an electron– Where does quadrupole come from?

• Quadrupole is generated by shear viscosity of photon-baryon fluid, which is generated by velocity gradient.

electronisotropic

anisotropic

no net polarization

net polarization

Boltzmann EquationBoltzmann Equation

• Temperature anisotropy, , can be generated by gravitational effect (noted as “SW” = Sachs-Wolfe)

• Linear polarization (Q & U) is generated only by scattering (noted as “C” = Compton scattering).

• Circular polarization (V) would not be generated. (Next slide.)

Primordial Gravity WavesPrimordial Gravity Waves• Gravity waves create quadrupolar temperatu

re anisotropy -> Polarization• Directly generate polarization without kV.• Most importantly, GW creates B mode.

Power SpectrumPower SpectrumScalar T

Tensor T

Scalar E

Tensor E

Tensor B

Polarization From ReionizatioPolarization From Reionizationn

• CMB was emitted at z~1088.• Some fraction of CMB was re-scattered in a reionized u

niverse.• The reionization redshift of ~11 would correspond to 3

65 million years after the Big-Bang.

z=1088, ～ 1

z～ 11, ～0.1

First-star formation

z=0

IONIZED

REIONIZED

NEUTRAL

Measuring Optical DepthMeasuring Optical Depth• Since polarization is generated by scattering, the

amplitude is given by the number of scattering, or optical depth of Thomson scattering:

which is related to the electron column number density as

Ne =

Polarization from ReioniazationPolarization from Reioniazation

“Reionization Bump”

• Outside P06– EE (solid)– BB (dashed)

• Black lines– Theory EE

• tau=0.09– Theory BB

• r=0.3

• Frequency = Geometric mean of two frequencies used to compute Cl

Masking Is Not Enough: Masking Is Not Enough: Foreground Must Be CleanedForeground Must Be Cleaned

Rough fit to BB FG in 60GHz

Clean FGClean FG

•Only two-parameter fit!

•Dramatic improvement in chi-squared.

•The cleaned Q and V maps have the reduced chi-squared of ~1.02 per DOF=4534 (outside P06)

BB consistent with zero after FG removal.

3-sigma detection of EE.

The “Gold” multipoles: l=3,4,5,6.

Parameter Determination: Parameter Determination: First Year vs Three YearsFirst Year vs Three Years

• The simplest LCDM model fits the data very well.– A power-law primordial power spectrum– Three relativistic neutrino species– Flat universe with cosmological constant

• The maximum likelihood values very consistent– Matter density and sigma8 went down slightly

What Should WMAP Say What Should WMAP Say About Flatness?About Flatness?

Flatness, or very low Hubble’s constant?

If H=30km/s/Mpc, a closed universe with Omega=1.3 w/o cosmological constant still fits the WMAP data.

Constraints on GWConstraints on GW• Our ability to

constrain the amplitude of gravity waves is still coming mostly from the temperature spectrum.– r<0.55 (95%)

• The B-mode spectrum adds very little.

• WMAP would have to integrate for at least 15 years to detect the B-mode spectrum from inflation.

What Should WMAP Say What Should WMAP Say About Inflation Models?About Inflation Models?

Hint for ns<1

Zero GW The 1-d marginalized constraint from WMAP alone is ns=0.95+-0.02.

GW>0The 2-d joint constraint still allows for ns=1 (HZ).

What Should WMAP Say What Should WMAP Say About Dark Energy?About Dark Energy?

Not much!

The CMB data alone cannot constrain w very well. Combining the large-scale structure data or supernova data breaks degeneracy between w and matter density.

What Should WMAP Say What Should WMAP Say About Neutrino Properties?About Neutrino Properties?

3.04)

• Understanding of– Noise,– Systematics,– Foreground, and

• Analysis techniques • have significantly improved

from the first-year release.

• A simple LCDM model fits both the temperature and polarization data very well.

• CMB offers constraints on:

• Neutrino properties: the number of species and mass

• Dark matter abundance

• Dark matter abundance and properties

• Inflationary models (flatness and spectral index)

• Reionization of the universe

• We are now working on the 5-year data…

SummarySummary