CMB Polarization and Cosmology
Wayne Hu KIPAC, May 2004 Outline • Reionization and its Applications Dark Energy The Quadrupole Gravitational Waves • Acoustic Polarization and Initial Power • Gravitational Lensing as Signal and Contaminant • Recent Polarization Collaborators: Christopher Gordon Matt Hedman Gil Holder Manoj Kaplinghat Takemi Okamoto Kendrick Smith Polarized Issues 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) Polarization from Thomson Scattering
• Quadrupole anisotropies scatter into linear polarization
aligned with cold lobe Hu & White (1997) Whence Polarization Anisotropy? • Observed photons scatter into the line of sight • Polarization arises from the projection of the quadrupole on the transverse plane
Hu & White (1997) Polarization Multipoles • Mathematically pattern is described by the tensor (spin-2) spherical harmonics [eigenfunctions of Laplacian on trace-free 2 tensor] • Correspondence with scalar spherical harmonics established via Clebsch-Gordan coefficients (spin x orbital) • Amplitude of the coefficients in the spherical harmonic expansion are the multipole moments; averaged square is the power
E-spin harmonic
Seljak & Zaldarriaga (1997); l=2, m=0 Kamionkowski, Kosowsky & Stebbins (1997) Reionization Temperature Inhomogeneity • Temperature inhomogeneity reflects initial density perturbation on large scales • Consider a single Fourier moment: Locally Transparent • Presently, the matter density is so low that a typical CMB photon will not scatter in a Hubble time (~age of universe)
observer transparent
recombination Reversed Expansion • Free electron density in an ionized medium increases as scale factor a-3; when the universe was a tenth of its current size CMB photons have a finite (~10%) chance to scatter
recombination
rescattering Polarization Anisotropy • Electron sees the temperature anisotropy on its recombination surface and scatters it into a polarization
recombination
polarization Temperature Correlation • Pattern correlated with the temperature anisotropy that generates it; here an m=0 quadrupole WMAP Correlation • Measured correlation indicates the universe remained at least partially ionized to a surprisingly large redshift or early time (z>10)
TE Cross Power 3 Reionization Spectrum ) 2
2 ( µ K π /2 l 1 +1)C l ( 0
-1 0 10 40 100 200 400 800 1400
Kogut et al (2003) Multipole moment (l) Why Care? • Early ionization is puzzling if due to ionizing radiation from normal stars; may indicate more exotic physics is involved
• Reionization screens temperature anisotropy on small scales making the true amplitude of initial fluctuations larger by eτ • Measuring the growth of fluctuations is one of the best ways of determining the neutrino masses and the dark energy
• Offers an opportunity to study the origin of the low multipole statistical anomalies • Presents a second, and statistically cleaner, window on gravitational waves from the early universe Ionization History Polarization Power Spectrum • Most of the information on ionization history is in the polarization (auto) power spectrum - two models with same optical depth but different ionization fraction
partial ionization step 500µK' 10-13 /2 π EE l
50µK' l ( +1) C
10-14
10 100 Kaplinghat et al (2002) [figure: Hu & Holder (2003)] l Principal Components • Information on the ionization history is contained in ~5 numbers - essentially coefficients of first few Fourier modes
0.5 x
δ 0
-0.5 (a) Best
0.5 x
δ 0
-0.5 (b) Worst 5 10 15 20 Hu & Holder (2003) z Representation in Modes • Reproduces the power spectrum and net optical depth (actual τ=0.1375 vs 0.1377); indicates whether multiple physical mechanisms suggested
0.8
x 0.4 -13 10 0 10 15 20 25 z /2 π EE l l ( +1) C 10-14 true sum modes fiducial
10 100 l Hu & Holder (2003) Total Optical Depth • Optical depth measurement unbiased • Ultimate errors set by cosmic variance here 0.01 • Equivalently 1% determination of initial amplitude for dark energy
102
101 prior 1 σµ 10-1 στ (cumul.) 10-2 prior 10-3
10-4 τµ 10-5 5 10 15 Hu & Holder (2003) mode µ 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
density gravitational perturbation wave Electric & Magnetic Polarization (a.k.a. gradient & curl) • Alignment of principal vs polarization axes (curvature matrix vs polarization direction)
E
B
Kamionkowski, Kosowsky, Stebbins (1997) Zaldarriaga & Seljak (1997) The B-Bump • Rescattering of gravitational wave anisotropy generates the B-bump • Potentially the most sensitive probe of inflationary energy scale
10
EE
1
∆ P ( µ K) BB
reionization recombination lensing maximum B-bump B-peak contaminant amplitude! 10 100 1000 l T/S, Inflation and the B-Bump • B-bump up to 20x more sensitive to T/S • In combination with recombination peak, constrain spectrum
10-1 τ=0.17 peak 10-2 16 idealized Planck 10 10-3 (GeV) T/S 10-4 bump 1/4 V 10-5
10-6 lensing contaminated 15 lensing partially removed 10 1 10 Hu (2001) Knox & Song (2002); Cooray et al (2002) noise (µK-arcmin) further: Hirata & Seljak (2003) Quadrupole Aside Low Quadrupole • Known since COBE: a ~2σ problem
6000 ) 2 ( µ K 4000 /2 π ΘΘ l l ( +1)C 2000
10 100 l ISW Spatial Modes • ISW effect comes from nearby acceleration regime • Shorter wavelengths project onto same angle Quadrupole Origins • Transfer function for the quadrupole
total 0.2
ISW Θ 2
T 0
SW -0.2 (a) Temperature
total 0.002 10
3 E 2 T 0 z<1
-0.002 (b) Polarization 0.0001 0.001 0.01 k (Mpc-1)
Gordon & Hu (2004) Lowering the Quadrupole • Transfer function for the quadrupole
0.2 Θ 2
T 0
-0.2 (a) Temperature
0.002 E 2
T 0
fiducial sound speed -0.002 cut-off (b) Polarization 0.0001 0.001 0.01 k (Mpc-1)
Gordon & Hu (2004) [Contaldi et al 2003; Hu 1998; Erikson et al 2002; Bean & Dore 2003] Low Quadrupole Models • Distinguished by polarization
fiducial ) 2 5 sound speed
( µ K cut-off
0 /2 π Θ E l
-5 l ( +1)C )
2 0.4 ( µ K 0.3 /2 π EE l 0.2
l ( +1)C 0.1
10 100 l Gordon & Hu (2004) [Dore, Holder & Loeb 2003] Low Quadrupole Models • Models: initial conditions vs. dark energy
fiducial 6000 sound speed cut-off ) 2 ( µ K 4000 /2 π ΘΘ l l ( +1)C 2000
10 100 l Gordon & Hu (2004) [Contaldi et al 2003; Hu 1998; Erikson et al 2002; Bean & Dore 2003] Initial Spectrum Transfer of Initial Power
Hu & Okamoto (2003) Prospects for Initial Conditions • Polarization crucial for detailed study of initial conditions, decade in scale of the acoustic peaks can provide exquisite tests of scale free initial conditions
Hu & Okamoto (2003)
cosmological 1 parameters fixed
0.1
fractional error temperature & polarization 0.01 even with large lever arm 0.01 0.1 other tests must k (Mpc-1) match accuracy Wang et al (1999); Kinney (2001); Miller et al (2002); Tegmark & Zaldarriaga (2002); Bridle et al (2003) Prospects for Initial Conditions • Polarization crucial for detailed study of initial conditions, decade in scale of the acoustic peaks can provide exquisite tests of scale free initial conditions
Hu & Okamoto (2003)
cosmological 1 parameters marginalized
0.1
fractional error temperature & polarization 0.01 even with large lever arm 0.01 0.1 other tests must k (Mpc-1) match accuracy Wang et al (1999); Kinney (2001); Miller et al (2002); Tegmark & Zaldarriaga (2002); Bridle et al (2003) Temperature and Polarization Spectra
100
10 reionization ΘE
1 EE
∆ ( µ K) BB
0.1 gravitational lensing gravitational waves 0.01 10 100 1000 l (multipole) Gravitational Lensing Gravitational Lensing • Gravitational lensing by large scale structure distorts the observed temperature and polarization fields • Exaggerated example for the temperature
Original Lensed Polarization Lensing Polarization Lensing • Since E and B denote the relationship between the polarization amplitude and direction, warping due to lensing creates B-modes
Original Lensed E Lensed B
Zaldarriaga & Seljak (1998) [figure: Hu & Okamoto (2001)] Temperature and Polarization Spectra
100
10 reionization ΘE
1 EE
∆ ( µ K) BB
0.1 gravitational lensing gravitational waves 0.01 10 100 1000 l (multipole) Lensing by a Gaussian Random Field • Mass distribution at large angles and high redshift in in the linear regime • Projected mass distribution (low pass filtered reflecting deflection angles): 1000 sq. deg
rms deflection 2.6' deflection coherence 10° Power Spectrum Measurements • Lensed field is non-Gaussian in that a single degree scale lens controls the polarization at arcminutes • Increased variance and covariance implies that 10x as much sky needed compared with Gaussian fields
0.02 realizations
0.01
0
-0.01 Gaussian variance
fractional power deviation -0.02
100 1000 Smith, Hu & Kaplinghat (2004) l Sample vs Noise Variance • Non-Gaussian sample variance doubles total variance at 4µK' for resolved B-modes 10
8 FWHM=1' 6 3'
4 10' ariance Degradation V 2 20'
1 10 ∆P (µK-arcmin) Reconstruction from Polarization • Lensing B-modes correlated to the orignal E-modes in a specific way • Correlation of E and B allows for a reconstruction of the lens • Reference experiment of 4' beam, 1µK' noise and 100 deg2
Original Mass Map Reconstructed Mass Map Hu & Okamoto (2001) [iterative improvement Hirata & Seljak (2003)] Matter Power Spectrum • Measuring projected matter power spectrum to cosmic vari- ance limit across whole linear regime 0.002< k < 0.2 h/Mpc
Linear 10–7 wer
10–8
deflection po Reference
∆P m ≈ −0.6 tot P eV 10 100 1000 L Hu & Okamoto (2001) [parameter forecasts: Kaplighat et al 2003] σ(w)∼0.06 Matter Power Spectrum • Measuring projected matter power spectrum to cosmic vari- ance limit across whole linear regime 0.002< k < 0.2 h/Mpc
Linear 10–7
10–8
deflection power Reference Planck
10 100 1000 L Hu & Okamoto (2001) [non-linear: see Amblard, Vale & White (2004)] σ(w)∼0.06; 0.14 Summary • CMB polarization generated by scattering alone and hence provides probes that are well localized in time and space • Early reionization provides a new window not only on the first generation of structure but also on gravitational waves, statistical anomalies on large scales, and calibration of fluctuations for dark energy studies • Acoustic polarization can provide exceedingly precise measurements of the initial power spectrum and any features that might exist in the decade of the peaks • Lensing of the acoustic polarization provides a means of reconstructing the mass distribution and hence constrain the neutrino mass and the dark energy