There's no question that for distant objects, one has to take into account the curvature of space-time to get the right answer for the redshift. For nearer objects, this just reduces to a relativistic doppler effect. When you start getting out to around a Hubble radius, however, this starts to become rather wrong and you have to take into account the space-time curvature.In several threads where I've seen the redshift issue discussed there's been some confusion about this point, Must we treat cosmological redshift as a purely kinematic (relativistic)doppler effect or as the time dymamics of the metric space? Or both views can be made to converge?