CMB Polarization
Understanding CMB Polarization
Beyond its temperature anisotropy, the cosmic microwave background carries a second, much fainter signal: a slight linear polarization. The physical cause is Thomson scattering. An electron scattering an incident radiation field that is brighter in one direction than another emits light with a net linear polarization aligned with the temperature gradient. At the surface of last scattering, density waves in the primordial plasma created exactly this kind of local anisotropy (specifically a quadrupole pattern), so the scattered radiation acquired a polarization of order a few microkelvin, roughly ten percent of the temperature fluctuations. Because the effect is tied to the same perturbations that seed cosmic structure, the polarization pattern is a clean and independent probe of early-universe physics.
Polarization on the sky is described by the Stokes parameters Q and U, which together give both the magnitude and the orientation of the linear polarization at each point. Q and U depend on the chosen coordinate axes, so cosmologists transform them into two rotationally invariant scalar fields, the E-mode and B-mode patterns, much as a vector field splits into curl-free (gradient) and divergence-free (curl) parts. This decomposition is powerful because different physical sources populate the two channels differently.
E-modes, B-modes, and the Measurement Challenge
E-modes are curl-free; their polarization vectors form radial or tangential patterns around temperature peaks. Scalar density perturbations produce E-modes, and they were first measured by the DASI experiment in 2002 and later mapped in detail by WMAP and Planck. B-modes carry a handedness that scalar perturbations cannot create. There are two B-mode sources: gravitational lensing, which bends E-mode polarization into a small B-mode signal on fine angular scales, and primordial tensor perturbations, gravitational waves from inflation, which would imprint a B-mode signal on large angular scales whose amplitude is set by the tensor-to-scalar ratio. Detecting the primordial component, at the level of tens of nanokelvin, is one of the hardest measurements in physics: it requires cryogenic bolometer arrays, rotating half-wave plates to modulate the polarization, multi-frequency observing to subtract polarized galactic dust and synchrotron foregrounds, and ruthless control of any leakage that turns the bright temperature signal into spurious polarization.
CMB Polarization Relations
P = √(Q² + U²), ψ = ½ arctan(U / Q)
Degree of polarization:
p = P / I (I = total intensity, Stokes I)
Tensor-to-scalar ratio:
r = power in tensor (gravitational-wave) modes / power in scalar modes
Where Q, U = linear Stokes parameters, P = polarized intensity, ψ = polarization angle, I = Stokes intensity, r = tensor-to-scalar ratio. Example: E-mode signal ~ few µK, current upper limits push r below about 0.03.
Polarization Mode Comparison
| Mode | Parity | Primary source | Amplitude | Status |
|---|---|---|---|---|
| E-mode | Curl-free | Scalar density perturbations | ~ few µK | Detected (DASI 2002) |
| Lensing B-mode | Curl | Lensing of E-modes | ~ 0.1 µK | Detected (2013 onward) |
| Primordial B-mode | Curl | Inflationary gravitational waves | < tens of nK | Not yet detected |
| Foreground (dust) | E and B | Polarized galactic dust | Frequency dependent | Subtracted via multi-band |
Frequently Asked Questions
What is CMB polarization?
It is a small linear polarization of the microwave background, a few microkelvin, about a tenth of the temperature anisotropy. It arises because Thomson scattering of the slightly anisotropic radiation field at last scattering produces net polarization. Measuring it means mapping the Stokes Q and U parameters and splitting them into E-mode and B-mode patterns.
What is the difference between E-modes and B-modes?
They are the curl-free and curl parts of the polarization pattern. E-modes come from scalar density perturbations and were detected in 2002. B-modes have a handedness scalar perturbations cannot make; primordial B-modes would come from inflationary gravitational waves, and a smaller B-mode arises when lensing distorts E-modes.
Why are CMB B-modes so hard to measure?
Primordial B-modes sit at tens of nanokelvin, far below the microkelvin E-modes and the 2.725 K mean. Detection needs ultra-low-noise cryogenic bolometers, strict control of instrumental polarization leakage, and multi-frequency removal of polarized dust and synchrotron foregrounds, as pursued by BICEP, Keck, and the Simons Observatory.