AI-generated illustration for Galileo Whispers of generic microwave-observing shielding and receiver housing in a snowy setting. It is not a named experiment or a polarization map, and the scene does not depict E or B modes.
E modes and B modes are two ways to describe the spatial pattern of linear polarization in the cosmic microwave background, or CMB. E patterns have even parity and B patterns have odd parity, in the mathematical sense used for the decomposition. The names do not mean that astronomers have divided the sky into ordinary electric-field and magnetic-field measurements.
Most importantly, a B-mode pattern is not, on its own, proof of primordial gravitational waves. A pattern has to be separated from gravitational lensing, foreground emission and instrumental effects before its physical origin can be inferred.
Start with an orientation, not a temperature color
A CMB temperature map assigns a temperature fluctuation to each sky direction. A polarization map also describes a preferred orientation of the light’s electric-field oscillation, together with its strength. One can draw a short line at each position to represent that orientation. The line has no arrowhead: turning it through 180 degrees gives the same linear polarization.
The origin is Thomson scattering by electrons. If radiation reaching an electron has the appropriate directional asymmetry—a quadrupole—the scattered light can acquire linear polarization. Hu and White’s 1997 polarization primer connects that scattering geometry with scalar, vector and tensor perturbations.
The measured quantities are usually Stokes Q and U. They depend on the axes chosen on the sky, much as the components of a vector depend on your coordinate system. Changing those axes changes Q and U without changing the physical light.
Two numbers at one pixel cannot label it E or B
For a simple illustration, let a polarization of strength P make an angle χ to a chosen axis. In a common convention, Q = P cos(2χ) and U = P sin(2χ). If P is one arbitrary unit, χ = 0 degrees gives Q = 1 and U = 0; χ = 45 degrees gives Q = 0 and U = 1. Doubling the angle expresses the 180-degree symmetry.
These are illustrative orientations, not measured CMB values. Neither pair says whether that pixel is an E mode or a B mode. That classification depends on how orientations and amplitudes vary across the surrounding map.
The all-sky analysis by Zaldarriaga and Seljak, section II, constructs E and B from the spatial polarization field. It removes dependence on arbitrary local coordinate axes. The familiar sketches of radial or tangential lines for E, and diagonally turned patterns for B, illustrate particular configurations; they are not a rule for identifying the origin of an individual drawn line.
What parity adds to the picture
Parity asks how a mathematical pattern behaves when spatial directions are inverted. E has the same parity family as an ordinary scalar temperature pattern; B has the opposite parity. On the full sphere, the corresponding multipoles transform with factors (−1)^ℓ for E and (−1)^(ℓ+1) for B.
This makes the geometry useful for physics. In linear theory, ordinary scalar density perturbations generate E polarization but no primordial B polarization before lensing is included. Tensor perturbations, including gravitational waves, can generate both. The important qualifiers are “linear” and “before lensing.” Dropping them turns a useful distinction into a false detection rule.
The 2025 Particle Data Group CMB review, section 29.7, sets out these distinctions and the differing parity factors. Our CMB overview supplies broader background on the ancient radiation; the E/B question concerns additional information in its polarization geometry.
Lensing can create B from an initially E-only sky
Intervening matter deflects the paths of CMB photons. This gravitational lensing remaps an existing polarization pattern: the directions from which we receive its features are displaced. The remapped pattern generally contains B as well as E, even if its original polarization was entirely E.
Zaldarriaga and Seljak’s 1998 lensing paper explicitly identified this conversion. It is a physical source of CMB B modes, not an instrumental mistake. Removing or modeling it is therefore part of a search for a weaker primordial contribution.
Galactic dust and synchrotron emission also have their own polarization patterns. Instrument calibration can mix components, and a sky mask complicates the mathematical separation. The geometry remains meaningful, but it cannot serve as a label reading “inflation” on every B-like feature.
A useful reading of a polarization result consequently keeps three levels separate: what Q and U were measured, how E/B power was reconstructed with its uncertainty, and which combination of physical sources explains that power. E and B make the map easier to compare with cosmological predictions. Evidence for any one origin requires the rest of that chain.
