Eight sky maps taken by different detectors of the Planck telescope resemble eight road atlases of the same city drawn by different cartographers. Each atlas is rotated by its own angle: one cartographer held the tablet slightly tilted, another slightly turned. If you overlay the atlases, the streets won't align. But if you know how each atlas is rotated, you can align them perfectly. This is exactly the problem scientists face when searching for cosmic birefringence, a tiny rotation of the polarization of ancient light that could reveal new particles.

The problem is that the rotation from a cosmic effect is indistinguishable from an error in detector alignment. If all detectors are rotated by the same angle, the sky picture rotates as a whole, and this common rotation is indistinguishable from a genuine cosmic signal. The existing Minami–Komatsu method uses the polarization of dust in our Galaxy to separate these two contributions. But that method relies on a dust model, and if the model is wrong, so is the calibration. The authors of the new work devised a check that doesn't use the dust model at all.

Their approach is like measuring distances between cities when you don't have a map with coordinates. If you measure the distance from Moscow to St. Petersburg, from St. Petersburg to Kazan, and from Kazan to Moscow, you can compute the triangle's angles without knowing where the triangle is on the globe. Similarly, the authors compare polarization maps in pairs. For each pair, they construct two combinations of spectra: symmetric and antisymmetric. The ratio of these combinations gives the difference in angles between detectors, while the common cosmic rotation cancels out completely. Then all pairwise differences are combined into a network where maps are nodes and angle differences are links. The network is solved by least squares, yielding a pattern of angles for all detectors.

The result of comparing 28 pairs of detectors is encouraging. The angles from the differential method and those from the Minami–Komatsu method agree: the chi-square statistic is 8.18 with seven degrees of freedom, corresponding to a probability of 0.32. All deviations are less than 1.8 sigma. This means that the calibration pattern given by the dust model is reproduced by a method that doesn't use that model. In other words, the dust model isn't fooling us: it yields the same angles as an independent approach based solely on the properties of the cosmic microwave background itself.

It's important to understand that this is not an independent measurement of the absolute value of the cosmic rotation. Both methods use the same sky maps, so the overall rotation is still indistinguishable from a common error. But now we know that the relative angles between detectors are correctly determined. This strengthens confidence in the measured value of cosmic birefringence of about 0.37 degrees. In future experiments such as Simons Observatory and LiteBIRD, this differential test can be applied as a standard check before releasing results.

Let's return to the atlases. If all cartographers rotated their tablets by the same angle, aligning the atlases is easy, but we won't know where true north is. For that, you need an external reference, like the North Star. In the case of Planck, such an external reference doesn't exist yet. But the differential test shows that all atlases are consistent with each other, meaning that any error, if present, is common to all. And that's a big step toward trusting the map.