TITLE: Local effects of cosmic expansion
QUESTION [5 upvotes]: Suppose we place two galaxies 100 Mpc apart, with zero initial velocity with respect to each other. In other words, they are static with respect to each other initially, with a negligible gravitational attraction, say. They are static is in the physical distance space, not necessarily in the comoving coordinate system.
Now, as the universe expands according to FRW metric, will the distance between the two galaxies increase with time as $d => a(t)d$?
If no, then is the expansion of universe really an expansion of space, or is it just that all matter are moving away from each other due to some initial explosion, like the big bang? Will the light emitted by one galaxy be redshifted to the other galaxy, as there is no relative velocity in the physical distance space, and hence no doppler effect?
If yes, then isn't it a violation of conservation of momentum? Two bodies initially with zero relative velocity and zero interaction suddenly starts to move away from each other? In that case, if the relative motion synchronises with the hubble expansion again with them receding away from each other, then what is the nature of the force/energy which is supplying the potential well to "glue" particles to the expanding comoving coordinate system?

REPLY [1 votes]: Expansion of space means that distance can increase between two particles with zero velocity. Because $d = d_{0}a(t)$, the particles themselves need not move. Imagine points, drawn on a balloon. As you inflate the balloon, distances increase, yet the points do not move relative to the balloon. This is what it means for the metric to evolve: the very definition of lengths is changing.
Let's suppose a length scale D for which the Universe is homogeneous, and two tracer particles at distance D with 0 co-moving velocity. As the Universe expands, the distance between the two will increase. Moreover, any photons in transit between the two galaxies will be redshifted--this is not a Doppler effect, this is an effect due to the spacetime metric changing. Neither particle moves relative to the co-moving coordinate system and neither gains momentum.
You must abandon the sense of cosmic expansion as a velocity--it is a change in distance without velocity. For $v = H_{0}d$ and $H_{0} \sim 70$ km/s/Mpc, what will you think when $H_{0}d = v > c$ at a measly distance of 4-5 Gpc? You know nothing can move faster than the speed of light. This is why General Relativity is the best way to describe the expansion of the Universe, with the understanding that there are no velocities greater than the speed of light, yet there are galaxies whose distances increase faster than 300,000,000 m/s.
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