If you look at a map of distant galaxies, it is not perfectly uniform: on one side of the sky there are slightly more, on the other — slightly fewer. This lopsidedness has been noticed in several sky surveys, and it does not look like a random fluke. Usually, it is explained by the fact that our Galaxy itself is flying somewhere, making distant objects appear shifted. But measurements do not always agree with this simple explanation.
The authors of the paper offer a different perspective. They consider not just the observer's motion, but their acceleration, as if we were not merely drifting with the current, but sometimes rowing sideways. In general relativity, such acceleration leaves an additional imprint on the light from distant galaxies: their redshift (the stretching of light due to the expansion of the Universe) acquires a peculiar 'patchiness'—slightly larger in one direction, slightly smaller in another. And this patchiness is not the same for all distances; it changes with depth.
This opens up a way to test: if the asymmetry in the galaxy distribution is caused only by ordinary motion, its dependence on distance will be one thing. If there is an additional acceleration of the observer, the picture will be different. Thus, one can separate 'ordinary' asymmetry from that which requires new physics.
Redshift was first noticed in 1912 by Vesto Slipher, but it was Edwin Hubble who explained it through the expansion of the Universe in 1929.