Cosmic Microwave Background Polarization:

The Next Key Toward the Origin of the Universe

©13700002003 Yuki D. Takahashi

Since the 1960s, humans on Earth have been able to study the cosmic microwave background (CMB) radiation left over from the Big Bang 14 billion years ago. The observed pattern of the CMB intensity across the sky has told us much about our universe, including its history, age, geometry, density,.... However, we still know very little, especially about the earliest moments of the Creation. We can learn about the first fraction of a second, among other things, by studying the polarization pattern of the CMB...

1. How did the Universe Begin? Inflation?

Currently the best theory we have about the earliest moment in the history of the universe is called "Inflation". During a tiny fraction of a second after the Big Bang, the universe seeems to have expanded exponentially, much faster than usual. This scenario explains several important observations about the universe:
  • Why the universe appears to have no overall curvature (flat).
  • Why the universe appears so isotropic.
  • Why there are structures in the universe.
  • Why we have not found cosmic relics like the magnetic monopoles.
Even though inflation conveniently explains these mysteries, we have no direct evidence that inflation is really what happened.


Did inflation happen?
How fast did the universe expand?
How can we explain inflation?

2. Inflation => Gravity Waves => CMB Polarization

The explosive expansion of space during inflation would have created ripples in the fabric of space. As explained below, these gravity waves should have left a signature in the polarization of the last-scattered photons (CMB).

The amplitude of the gravity wave is proportional to the expansion rate H during inflation, which in turn is proportional to the inflation energy scale squared:

GW amplitude ∝ H ∝ Einf2, where Einf~<1016GeV

But how did gravity waves cause CMB polarization?

3. Why is CMB radiation polarized? <= Anisotropic Scattering

The CMB radiation is polarized because it was scattered off of free electrons during decoupling.

colder radiation ↓
hotter radiation →
Hu 2001
When an electromagentic wave is incident on a free electron, the scattered wave is polarized perpendicular to the incidence direction. If the incident radiation were isotropic or had only a dipole variation, the scattered radiation would have no net polarization. However, if the incident radiation from perpendicular directions (separated by 90°) had different intensities, a net linear polarization would result. Such anisotropy is called "quadrupole" because the poles of anisotropy are 360°/4 = 90° apart.

But why was there quadrupole anisotropy?

4. Quadrupole (90°) Temperature Anisotropy at Decoupling

At radiation decoupling when photons last scattered off of electrons, there was temperature inhomogeneity (shown in the animation as a pattern of red and blue). When recombination proceeded to the point where photons from hot and cold regions could meet to be scattered by the same electron, the scattered radiation were polarized. For example, for an electron at the center of the middle circle, photons (yellow) diffusing from vertical directions are hotter (blue) while photons from horizontal directions are colder (red). Comparing this situation with the above animation, the net polarization of the scattered radiation is horizontal (green line).

This photon diffusion into regions of different temperatures were possible only when the plasma became optically thin enough during recombination. Also, these diffused photons could scatter only while there are still free electrons left. Thus, polarized radiation could be produced only during a short period near the end of recombination. Only a small fraction of the CMB radiation is therefore polarized.

Electrons at different locations (at the center of different rings in the animation) would produce different polarization orientations and magnitudes. As observed today, the CMB polarization varies across the sky. The quadrupole anisotropies at decoupling are projected into CMB polarization pattern. Since photons could not diffuse too far, polarization doesn't vary much across very large angular scales.

What else could cause quadrupole anisotropy?

5. Quadrupole Anisotropy <= Perturbations

The quadrupole anisotropy (which produced CMB polarization) could arise from 3 types of perturbations:

Hu 2001

Scalar perturbation: Energy density fluctuations in the plasma (resulting in hotter and colder regions) cause velocity distributions that are out of phase with the acoustic density mode. The fluid velocity from hot to colder regions cause blueshift of the photons, resulting in quadrupole anisotropy.

Vector perturbation: Vorticity in the plasma cause Doppler shifts resulting in the quadrupole lobes in the figure. However, vorticity would be damped by inflation and is expected to be negligible.

Tensor perturbation: Gravity waves stretch and squeeze space in orthogonal directions (as shown by the test 'circles' in the figure). This also stretches the wavelength of radiation, therefore creating quadrupole variation in incoming radiation temperature. Gravity waves from inflation would produce tensor perturbation!

6. How can we Study the Polarization Pattern?

The polarization pattern in the sky can be decomposed into 2 components:

The E-mode may be due to both the scalar and tensor perturbations, but the B-mode is due to only vector or tensor perturbations because of their handedness.

E-mode: G (grad) no-handed <= Scalar / Tensor perturbations
B-mode: C (curl) handed <= Vector / Tensor perturbations

Seljak & Zaldarriaga
↑ pure E-mode           pure B-mode ↑

7. Polarization Anisotropy Spectrum

Once we have maps of the E- and B- components (and the temperature anisotropy), we can analyze them by decomposing them in terms of spherical harmonics. For example, for temperature anisotropy Θ ≡ ΔT/T:  
The multipole moments are used to define the power spectra:
(The B-mode is not expected to correlate with E or Θ because of its handedness.)
Each of these can be scaled to give a corresponding magnitude in temperature scale: =>

The upper curve (black) is the most familiar temperature anisotropy spectrum, with amplitudes 5 orders of magnitude smaller than the CMB temperature of 3 K.

The polarization signals (EE,BB) are smaller by an additional 1~2 orders of magnitude because the polarized radiation were produced only near the end of recombination. The polarization spectra decline at large angular scales (low l) because photons couldn't diffuse so far before the end of recombination.

Hu&Dodelson 2002

(The multipole index l corresponds to angular scales of 180° / l.)

Since the E- and B- polarization modes come from different physics, the anisotropy spectra for the two components are expected to have different shapes and amplitudes.

8.   E-mode (DASI 2002 !),   TE correlation (WMAP 2003 !)

Since the velocity gradients in the plasma (which is out of phase with the density fluctuations) produced the E-mode polarization, the polarization spectrum is directly out of phase with the temperature anistropy spectrum. These two spectra are therefore correlated (TE correlation). The E-mode peaks around an angular scale corresponding to the photon mean free path at decoupling.
The E-mode was first detected in 2002 by DASI!

The signal level was consistent with the prediction based on the measured temperature anisotropy.

TE correlation was measured by WMAP, matching the predicted spectrum and showing the reionization signature!

Re-scattering of the CMB photons during reionization added to the polarization spectrum at large angular scales (l < 10). The observation indicates that reionization happened at redshift around zr = 11~30.

9. Gravity wave B-mode (200?)

The most profound will be the detection of B-mode polarization due to gravity waves from the inflation at the beginning of the universe.

Hu et al 2003

Based on the WMAP data, all we know is that the energy scale of inflation must have been < 3x1016 GeV (Kaplinghat 2003). When we detect the gravity wave signal, we will be able to find the energy scale of the very first major event only 10-35 second after the Creation of our universe.

2003/10 Kaplan, Delabrouille, Fosalba, Rosset CMB Polarization as complementary information to anisotropies
2003/5 Zaldarriaga: The Polarization of the Cosmic Microwave Background
2002/10 Hu: CMB temperature and polarization anisotropy fundamentals (Annals of Physics)
2002/9 Hu & Dodelson: Cosmic Microwave Background Anisotropies (Annual Review)
2002/9 Kamionkowski: Gravitational Waves and CMB Polarization
2002/3 Gangui: Topological defects
2001 Hu: CMB tutorial (intermediate)
1999 Kosowsky: Introduction to Microwave Background Polarization
1996 Hu & White: A CMB Polarization Primer
1996 Hu: A Tour of CMB Physics
1996 Hu: An Introduction to the Cosmic Microwave Background (beginners)
Wayne Hu
2003/9 Scientific optimization of a ground-based CMB polarization experiment (Bowden et al)
2003/8 Status of CMB Polarization Measurements from DASI and Other Experiments (Carlstrom, Kovac, Leitch, Pryke)
201?: Inflation Probe
2007: Planck
2005 [GW]: BICEP
2005 [lense]: PolarBeaR
2005 [lense]: QUEST (Stanford) (QUaD)
2004: AMiBA
2003: CAPMAP (Princeton) Chicago
2003 [E]: MAXIPOL
2003 [TE]: WMAP
2002 [E]: DASI (Chicago)