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New-ish measurements from Hubble + Webb say that the Universe is expanding at different rates everywhere: https://www.livescience.com/space/cosmology/james-webb-telescope-confirms-there-is-something-seriously-wrong-with-our-understanding-of-the-universe

Why is this actually surprising?

According to mainstream GR, there is no difference between gravity and spacetime curvature which varies everywhere there are massive objects.

If spacetime is bent e.g. around black holes at galactic cores and the curvature also varies over time with objects moving around like a water surface forming currents or waves that rise and recede, wouldn't this also affect the measured velocity of expansion wherever you look out into the sky like measurements of ocean currents at local scales would be affected by waves or cross currents?

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What makes you think the measured expansion of space is different in different places? Most studies suggest that on a large (cosmological) scale it is remarkably uniform. There was a suggestion a few years back that it might not be; this got a lot of attention in the press but doesn't seem to have held up.

Note also that spacetime curvature due to black holes or even individual galaxies is very small when compared with cosmological distances.

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  • $\begingroup$ According to this article it wasn't just confirmed but "the possibility of any measurement error [was put] to bed for good" livescience.com/space/cosmology/… $\endgroup$ Commented Mar 22 at 14:21
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    $\begingroup$ The "where we look" in that article appears to be about the methods of measurements (Cepheid variables vs cosmic microwave background) rather than direction. In any case it's always wise to take any statement in a popular article with a huge grain of salt. $\endgroup$
    – Eric Smith
    Commented Mar 22 at 20:58

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