I don't think that's true. Expansion is not very weak around matter, it just doesn't exist. It sounds a little counter intuitive to think that expansion "shutdowns" as we get closer to galaxy. But that's because expansion and gravity are a little more complicated that just a force.
We over simplify what expansion really is, which leads to this type of thinking.
Expansion and gravity are results of the same equations.
Einstein equations are difficult to use, so we usually split the results in two models, FLRW (empty space) and Schwarzschild metrics (around matter). Computing the equations leads, respectively, to expansion and gravity. And it's not like there's one and the other, with gravity fighting expansion. It's "one or the other".
Around matter (in Schwarzschild metric), solving Einstein questions, we see zero expansion drifting. If there is matter, there is gravity, and no expansion.
Quoting Wikipedia [1]:
> Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so
> Einstein equations are difficult to use, so we usually split the results in two models, FLRW (empty space) and Schwarzschild metrics (around matter). Computing the equations leads, respectively, to expansion and gravity. And it's not like there's one and the other, with gravity fighting expansion. It's "one or the other".
Arguably splitting a complex model of reality in two for convenience and saying that it’s “one or the other” is also an over simplification.
By the way, the same wikipedia entry also says things like “gravity binds matter together strongly enough that metric expansion cannot be observed on a smaller scale at this time.”
We over simplify what expansion really is, which leads to this type of thinking.
Expansion and gravity are results of the same equations.
Einstein equations are difficult to use, so we usually split the results in two models, FLRW (empty space) and Schwarzschild metrics (around matter). Computing the equations leads, respectively, to expansion and gravity. And it's not like there's one and the other, with gravity fighting expansion. It's "one or the other".
Around matter (in Schwarzschild metric), solving Einstein questions, we see zero expansion drifting. If there is matter, there is gravity, and no expansion.
Quoting Wikipedia [1]:
> Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so
[1]: https://en.wikipedia.org/wiki/Expansion_of_the_universe#Effe...