Yes, that's right. There are a couple of different ways to measure that now.My understanding is that the rate of expansion appears to be increasing?
There is curvature anywhere there's matter (or energy), so that's not really an issue. When we say the universe is flat (in space), we mean on average over very very large regions. But there is curvature, for example, around galaxies. In any case, while the average universe is expanding, bound objects, like galaxies are stuck together --- space is not expanding between the stars of our galaxy, for example.But, I have always had the same question: At what scale does expansion occur? Uniform expansion implies odd effects in bound systems. On the other hand, non-uniform expansion seems to imply curvature between the expanding regions and the non-expanding regions.
You have to be careful what you mean by a bound system, and the statement is a little vague. Consider a galaxy: the stars are "bound" in the sense that they are not moving quickly enough to escape from each other (in the same way that a rocket has to be moving at a certain speed to escape the earth). And there are small galaxies close to our galaxy that are bound in the same way. Even if you applied Hubble's law on these scales, the expansion speed you'd find would be very small compared to the speeds of the bound objects, so it is irrelevant. You'd expect the structure of spacetime in a galaxy to just be that for a bunch of matter in a non-expanding universe.Also, the scale at which gravity still has an effect, say, for a galaxy, is quite large, and never quite goes away - it's just overwhelmed at a distance by the fields from other masses. I don't understand how there wouldn't be an an expansion within some bound system.
However, if you are talking about two far-apart galaxies, yes, they can be gravitationally bound in the sense that they will eventually collapse together but still have some expansion in between. For example, our galaxy is expected to eventually fall into (and merge with) the galaxies of the Virgo Cluster, and, in fact, we are moving closer to them. But the overall expansion of the universe isn't entirely negligible when we look at our motion relative to those galaxies, either.