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.