Space time expansion near galaxies I understand that on galactic scales, the expansion of space time has no appreciable effect, gravity being dominant and thus distance between stars remains fixed despite universal expansion. 
Can anyone help me see this mathematically? I have been unable to find equations to show me both gravity and expansion together. I am interested in whether individual mass objects far from the virial mass centre would start to be caught in the space time expansion and thus end up farther from the galactic centre, i.e. some boundary condition where expansion does overcome gravity due to gravitational effects being weaker at the furthest fringes of matter attracted by the central masses.
 A: One way to see this is simply to note the value of the Hubble constant, about 
$70\rm\,km/(s\cdot Mpc)$.  The Milky Way galaxy is about 0.030 Mpc in diameter, so the Hubble "flow" from one end of the Milky Way to the other is only about 2 km/s.  This is much smaller than the "peculiar" motions of objects within the galaxy.  Heck, the eastward motion of Earth's surface near the equator is about 0.5 km/s.
Compare this to low-temperature phenomena in other areas of physics.  If you're interested in milli-electronvolt physics, you can't explore it at room temperature ($kT = \rm25\,meV$); you have cool your material off to get rid of the random thermal motions.
Extending to the Local Group: the Andromeda galaxy and its satellites are approaching us at about 100 km/s, from sort-of a megaparsec away.  So the "thermal motion" of galaxies in the Local Group is comparable to the Hubble flow, but still "hot" enough that the directions are more or less random.
Thriveth points out a subtle corollary in comment below: since there is no real distinction in GR between "expansion of matter within spacetime" and "expansion of spacetime carrying matter along," it is reasonable to conclude that within a galaxy, where motions are rapid and randomly oriented, there is no spacetime expansion at all.  I admit to being somewhat out of my depth here.
