# Why do gravitationally bound regions not feel the expansion of the universe but the rate of expansion of the universe does depend on gravity?

From Wikipedia,

The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time,

implying that gravitationally bound regions are not affected. I have heard this statement here on StackExchange, too.

However, from Friedmann's second equation, $$\frac{\ddot{a}}{a} = -\frac{4 \pi G}{3}\left(\rho+\frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3}$$, gravity is presumably factored in through the energy density term $$ρ$$.

Question: why are the influences of gravity and expansion of space asymmetric? Or they are and my logic is simply flawed? If so, how is it flawed?

• You cannot use Friedman’s equation on local scales where the metric is not described by an FRLW universe. – gmarocco Nov 14 '19 at 13:30
• @gmarocco Could you expand on that just a bit and post that as a separate answer so that I can tick it? For example, is it true that local changes in gravity have no effect on the local rate of expansion of the universe? If the answer is 'yes', that would solve the problem of symmetry and answer my question. – Max Nov 14 '19 at 13:34
• They are affected, just not by much. Imagine the expansion of space trying to stretch a spring. – m4r35n357 Nov 14 '19 at 13:37
• Sure I’ll do so shortly. – gmarocco Nov 14 '19 at 13:38
• duplicate or near duplicate of physics.stackexchange.com/questions/70047/… – Ben Crowell Nov 14 '19 at 15:00