[Beldin]

Just curious, since gravity works over infinite distances (as I understand things):

When do two masses stop being gravitationally bound? Is that when each mass's relative speed exceeds the escape velocity of the other mass?

No, that can't be right: they could still end up in orbit - obviously gravitationally bound.

[jjk166]

In this case, bound means that the force of gravity is stronger than the expansion of space time. All of space is expanding, but things that are close (ie within a few hundred thousand light years) pull on eachother enough to resist being swept away by the "current" and only distant galaxies recede. But it's not like there is something special about our position, if you could magically teleport to another galaxy a few billion lightyears away the picture would be about the same: your own galaxy and those nearby don't go flying apart, but all the distant galaxies do.

[goalieca]

One complication is that since the universe is homogenous and infinite, there’s a boundary that is expanding away from us faster than the speed of light and this gravity as well.

[errcorrectcode]

The observable universe is of finite mass and size, while the total universe is of infinite or finite mass and size. On a macro scale, the total universe probably looks similar. It's definitely not micro homogeneous or entropy would be infinite and heat death would have already occurred. Heat death won't be the biggest problem because of the likelihood of the Big Rip.