I assume you mean is fracdvdt the same for all objects and/or is it constant for all objects, where v is recessional velocity (and t is cosmic time)? The answer is no it is not the same for all objects and it is not constant for all objects.
v=fracdDdt=H(t)D
Where D is proper distance and H(t) is the Hubble parameter. If we take the Hubble parameter as a constant, then:
D=D0eHt
Where D0 is the proper distance at the present time. So,
D″(t)=fracdvdt=D0H2eHt
So the "recessional acceleration" of an object depends on its present proper distance and is exponentially increasing with time.
Now the Hubble parameter isn't a constant and in LCDM cosmology is currently asymptotically decreasing to a constant. In the current epoch though it is fair to say that the "recessional acceleration" of an object depends on its proper distance and is increasing with time.
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