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It has been proposed the Hubble tension can be solved if we assume our galaxy is located in a giant void (such as KBC). I am confused at this point. If we were living in a giant void, we should have measured the Hubble constant lower. Since when the light passes an underdense region it gets less redshifted. Less redshift means less expansion or lower Hubble constant right? But we are measuring it higher. So shouldn't we live in a more dense region rather than an underdense region, to explain the discrepancy? What am I missing here?

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If we are in a void, then the matter density is lower and hence expansion is faster locally. Matter density decelerates the expansion. Thus locally the Hubble parameter is larger than when measuring say high redshift supernovae in a more distant part of the universe.

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The "void" in concern is commonly referred to as "Hubble bubble". Below is explanation from wiki on Hubble bubble:

In accordance with the Copernican principle that the Earth is not in a central, specially favored position... If, on the other hand, Earth were at or near the center of a very low-density region of interstellar space (a relative void), denser material in a shell around it would strongly attract material away from the centerpoint. Thus, stars inside such a "Hubble bubble" would accelerate away from Earth much faster than the general expansion of the universe.

As you can see, the key to the "Hubble bubble" is the denser material in a shell beyond the bubble which pulls things within the bubble away from Earth faster. Apart from the technical minutia (for instance, where the heck is the edge of the bubble?), the "Hubble bubble" thesis is especially distasteful in abandoning the Copernican principle. But truth hurts, as aptly worded by Lizzo: maybe Earth just took a DNA test, turns out it's 100% the center of the universe.

Note that the "Hubble bubble" line of thought is to change the Friedmannian cosmology at low redshift (since local bubble pertains to the low redshift observations), while most of the other proposed fix to the 'Hubble tension' is to tinker with the early universe via fudging the high redshift parameters (like a bit more dark energy here and a touch of jalapeno there).

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    $\begingroup$ The "extra" velocity that galaxies would have inside the void is not due to gravity from a shell around the void, but an actual larger expansion rate of space, i.e. a larger value of $H_0$, because of the smaller local value of $\rho$ entering the Friedmann equation. $\endgroup$
    – pela
    Feb 4, 2020 at 23:14
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    $\begingroup$ The shell theorem ensures that a shell exerts no net attraction on anything within it. The Wikipedia explanation is incorrect. $\endgroup$
    – ProfRob
    Feb 5, 2020 at 6:47
  • $\begingroup$ @RobJeffries,is the shell theorem still valid for a non-static metric? $\endgroup$
    – MadMax
    Feb 5, 2020 at 18:15
  • $\begingroup$ @MadMax "denser material in a shell around it would strongly attract material away from the centerpoint." and "the denser material in a shell beyond the bubble which pulls things within the bubble away from Earth faster". These are (incorrect) Newtonian arguments. $\endgroup$
    – ProfRob
    Feb 5, 2020 at 19:07
  • $\begingroup$ @RobJeffries, given the non-static metric, is the argument in wiki Newtonian? In other words, should the wiki arguments be validated (or invalidated) in the Newtonian context? $\endgroup$
    – MadMax
    Feb 5, 2020 at 19:11

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