Not necessarily. Two objects can be locally stationary and yet have a redshift w.r.t. each other. No motion is necessary if space expands.
Indeed. I have also wondered about the effect of gravity on redshift. My inspiration is Einstein's illustration of the equivalence principle. In an elevator, you cannot tell if there is gravity and you are stationary OR if the elevator is accelerating upwards. So extending this analogy to the universe, we should have the same problem.
Is spacetime expanding or is it under the influence of a strong gravitic field?
Where would this gravity come from? dark matter. Especially since so much dark matter exists in the universe, the gravitic contribution to redshift should be significant. Since dark matter is not observable with EM, and there is SO MUCH of it in the vastness of space, it follows there is a strong gravitational field in space where we see nothing else. The effect of gravity on doppler shift is no different than the effect of an accelerating spacetime expansion. Well, maybe the magnitude of the effect is different but then that the depends on the acceleration of spacetime expansion.
Ever since vera rubin, there have been tantalizing paradoxes about galactic velocities. Is it possible when looking at these vast scales of distance that 'dark gravity' is affecting the speed of light. Yes, I said it. Dark Gravity. That would be the force generated by dark matter. Of course, the evidence for the existence of dark matter began with measurements of orbital velocities and the inferred gravitational forces. When these forces far exceeded the observed mass, we postulated dark matter. Certainly, alternative explanations like a non-constant gravity have been entertained although I am unclear on the data that refuted them. So, really, dark gravity, per se, does not exist, but rather I am referring to that component of gravity that derives from dark matter.
My point is that maybe spacetime is not expanding at an accelerating rate, maybe it just *appears* so, due to dark gravity.