The standard model of Cosmology makes an important assumption: that the Universe is essentially isotropic, the same in all directions. This is a pretty good assumption, and so far isotropy seems to be the case. The Cosmic Microwave Background radiation we see coming from all directions has some small blips in it, indicating minor deviations from isotropy, but nothing to write home about. So far so good.
But we don’t know for sure just how far that isotropy extends. If there were huge deviations, it would mean we live in a wholly different universe from the one we thought we did. This class of alternative universes is known as Bianchi cosmologies, and only a few of them have been tested against the data. That leaves plenty that haven’t. If our Universe turns out to be a Bianchi universe, it would rule out our standard cosmology and associated ideas, such as inflation.
In an attempt to find out what kind of universe we live in, a group of researchers constructed a more general test. If the Universe is truly anisotropic (different in different directions), it would mean it’s expanding at different rates. If so, light traveling through these differently expanding regions would be red-shifted differently. That's because the wavelength of light is stretched as it moves through expanding space, so if space were expanding at different rates, the redshift would be altered accordingly.
Any differences, were they to exist, should be detectable. The trick is disentangling that effect from the influence of all the early Universe’s chaos, which also affected the Cosmic Microwave Background.
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