How fast are we moving? The puzzle of our velocity from radio galaxies

The temperature of the cosmic microwave background (CMB) – an echo from the Big Bang – is isotropic to 1 part in 10^5. An exception is the dipole term, of roughly 100x larger amplitude than the other multipoles. The standard interpretation is Doppler effect due to our (observer) motion with respect to the CMB, with velocity of about 370 km/s. Its components are motion of the Sun in the Milky Way (MW), of the MW towards the barycenter of the Local Group (LG) of galaxies, and of the whole LG in the ‘cosmic rest frame’. As shown first by Ellis & Baldwin (1984), such motion should induce relativistic dipole effects in the counts of isotropically distributed radio sources at cosmological distances. Measurements of this effect have been done for more than 2 decades, but are abundant only in the recent years, thanks to the availability of wide-angle, deep radio surveys. The general outcome of these measurements from many different experiments is a big surprise: while the direction of such a dipole is usually consistent with that of the CMB, the associated amplitude is a few times larger and would indicate our motion of v>1000 km/s. I will present the context of such measurements in the standard cosmological model, summarize the current results, and describe our recent contribution from Böhme et al. (2025, PRL), where the resulting amplitude is >3.5 times larger than expected from CMB. So far, no systematic effects have been found that could explain such a puzzling result. Finally, I will mention some other ways of probing our motion with respect to the large-scale structure of the Universe, and the near-term prospects for such measurements.