I'm trying to make a point that there is curvature of spacetime from the metric expansion that contributes to the dynamics of a galaxy. This curvature would be in addition to the curvature caused by the visible mass/energy content of the galaxy. I got back a note from an editor saying
"In the language of relativity physicists, “locally flat”, also called “locally Lorentz”, means flat at first order in separation from any chosen point. Of course, at second order one sees the influence of the Riemann curvature tensor, i.e. of the curvature."
Can someone interpret this for me? When a book says that the local geometry of spacetime is flat, how local is that? Microscopically, the size of a football field, a solar system, a galaxy? What's the cutoff for a 'local' geometry?