Cosmological expansion of space - question

[elcaro]

TL;DR Summary

The Lambda-CDM cosmological models builts on the idea that some (still unknown) physical phenomena (called 'Dark energy') is responsible for the expansion of spacetime and even the relatively recent accelerated exapansion of spacetime. But gravitationally bound objects (solar system, galaxies) do not experience spacetime expansion. So, my question is: is the expansion of spacetime gradual or is there a sharp division between non-expanding and expanding regions of space-time?

I the lambda-CDM model, is the expansion of spacetime uniform around all of spacetime, is there a smooth transition between expanding parts of spacetime (the voids) and non-expanding parts of spacetime, or is there a sharp distinction between expanding and non-expanding parts of spacetime.
Is the gravitational constant (G) the same in all of space, or does it depent on the rate of expansion of spacetime?

 

[PeroK]

TL;DR Summary: The Lambda-CDM cosmological models builts on the idea that some (still unknown) physical phenomena (called 'Dark energy') is responsible for the expansion of spacetime

Technically it's the expansion of space. This is a consequence of GR and does not require dark energy.

and even the relatively recent accelerated exapansion of spacetime.

The accelerating expansion is caused by dark energy.

But gravitationally bound objects (solar system, galaxies) do not experience spacetime expansion. So, my question is: is the expansion of spacetime gradual or is there a sharp division between non-expanding and expanding regions of space-time?

For any region of space, you have a certain mass density and radiation density. That determines the dynamics of that region. For gravitationally bound systems, the mass dominates.

For a larger scale region, the dark energy may dominate. There is no sense in which you have a boundary or transition, but as you increase the size of the region you are studying, so the overall dynamics change.

Is the gravitational constant (G) the same in all of space, or does it depent on the rate of expansion of spacetime?

G is essentially a conversion factor relating mass units to space units. You can specify units where $G =1$. In those terms, the question does not make sense.

 

[Ken G]

Could you specify that G is 1 everywhere and everywhen if it wasn't in fact constant? I think it would have to be a real constant in order to be able to do that, so the question should still make sense. In other words, one can imagine universes where it is not possible to take G to be 1 everywhere without changing other things as well, like the mass of the particles. So if it is always the product of G with M that serves as the source of gravity, the question would be, can the same object placed at a different place or time have a different G*M? That would be a break in a symmetry that I would think would have observable consequences, but has not as yet been in evidence.

 

[PeterDonis]

In the lambda-CDM model, is the expansion of spacetime uniform

With @PeroK's correction that it is the expansion of space, yes. That is because the Lambda-CDM model ignores the actual inhomogeneities in the density of stress-energy and treats the universe as having uniform density. This is an approximation. In this approximation, gravitationally bound systems do not exist (more precisely, their presence is ignored as having an insignificant effect on the global dynamics of the universe).

Is the gravitational constant (G) the same in all of space

Here the opposite correction to @PeroK's applies: in GR, G is constant in all of spacetime. Other theories have been proposed that allow G to not be constant, but as has been noted, we have no evidence for any such thing so no such theory has gotten any traction.