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We normally assume that the recession of distant galaxies is due to the expansion of the space between the galaxies and us.

In a co-moving frame the expansion of space is factored out so that all objects remain at a fixed distance away from us in cosmological time. Thus the co-moving frame is equivalent to our local inertial frame extrapolated out to large distances.

In this co-moving frame, at the present cosmological time, the Hubble law defines a velocity field that increases linearly with distance away from us according to the expression:

v(t) = H_0 r(t).

where H_0 is the present value of the Hubble parameter and t is our local time.

Can these velocities be taken to be "true" velocities relative to us such that the proper time for a galaxy, at distance r moving with velocity v, is relativistically dilated compared to our local time?

John

In a co-moving frame the expansion of space is factored out so that all objects remain at a fixed distance away from us in cosmological time. Thus the co-moving frame is equivalent to our local inertial frame extrapolated out to large distances.

In this co-moving frame, at the present cosmological time, the Hubble law defines a velocity field that increases linearly with distance away from us according to the expression:

v(t) = H_0 r(t).

where H_0 is the present value of the Hubble parameter and t is our local time.

Can these velocities be taken to be "true" velocities relative to us such that the proper time for a galaxy, at distance r moving with velocity v, is relativistically dilated compared to our local time?

John

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