Field Note: Polarization of the CMB
E-modes and B-modes
The cosmic microwave background is not just a temperature map. It is also polarized.
This polarization is subtle — a fractional effect on the order of microkelvins — but it carries information that temperature fluctuations alone cannot provide. It was first definitively detected by the DASI experiment at the South Pole in 2002, and since then has been measured with increasing precision by WMAP, Planck, and a suite of ground-based and balloon-borne instruments.
Where Does It Come From?
CMB polarization arises from the same process that produces the temperature anisotropies: Thomson scattering of photons off free electrons in the early universe. But there's a crucial difference. Polarization is generated only when the incoming radiation field has a quadrupole anisotropy when viewed from the electron's rest frame. A perfectly isotropic radiation field produces no polarization. A dipole anisotropy produces none either. You need that quadrupole — the radiation needs to be hotter in some directions and colder in others in a very specific pattern.
In the early universe, these quadrupoles were generated by the acoustic oscillations themselves. The compression and rarefaction of the primordial plasma naturally created the anisotropic scattering geometries needed to polarize the photons.
E-modes: The Gradient Pattern
E-mode polarization is the first type to be understood theoretically and the first to be observed. It produces a curl-free pattern on the sky — analogous to the electric field of an electrostatic charge distribution, hence the name. In Fourier space, E-modes couple to the density perturbations in a way that makes them highly predictable within the standard cosmological model.
The E-mode angular power spectrum has been measured with exquisite precision. It shows a series of acoustic peaks and troughs that complement the temperature spectrum. The first E-mode peak occurs at roughly the same angular scale as the first temperature peak, but the relative amplitudes of the peaks carry different physical information — notably, they are sensitive to the optical depth to reionization.
The Planck satellite measured E-modes up to multipole moments of ℓ ≈ 2500 with extraordinary precision. These measurements provide independent constraints on the cosmological parameters derived from the temperature power spectrum and, when combined with temperature data, dramatically sharpen those constraints.
B-modes: The Curl Pattern
B-modes are the holy grail of CMB polarization. They produce a curl-like pattern — analogous to magnetic field lines from a current distribution. In the standard model, B-modes are generated at very low amplitude primarily by gravitational lensing of E-modes by large-scale structure. The lensing B-mode signal was first detected by the SPT and ACT experiments around 2014, and it has been measured by numerous subsequent experiments.
But there's another source of B-modes that cosmologists desperately want to see: primordial B-modes generated by gravitational waves from cosmic inflation. Inflation predicts a stochastic background of tensor perturbations — gravitational waves — that would imprint a characteristic B-mode signal on the CMB with a peak at large angular scales (ℓ ≈ 80). The amplitude of this signal is parameterized by the tensor-to-scalar ratio, r. Detection of primordial B-modes would be direct evidence for inflation and would measure the energy scale at which inflation occurred.
The BICEP2 collaboration's 2014 announcement of a detection — r ≈ 0.2 — proved to be contaminated by Galactic dust. The Planck collaboration subsequently showed that the dust signal could fully explain the observed signal. The quest continues. Current upper limits from BICEP/Keck place r < 0.036. Future experiments aim to reach r ≈ 0.001.
Why Polarization Matters
CMB polarization matters because it probes different physics than temperature does. E-modes tell us about the velocity field of the primordial plasma at last scattering. B-modes tell us about gravitational waves, lensing, and potentially new physics beyond the standard model. The polarization signal also provides a way to break parameter degeneracies that limit the precision of temperature-only analyses.
In the end, polarization transforms the CMB from a static photograph into a dynamic record of how the early universe moved, flowed, and rippled.