In article ,
Phillip Helbig---undress to reply writes:
Consider the de Sitter universe, which has a cosmological
constant and no matter. The expansion law is exponential, i.e. the
acceleration increases with time. Since the Hubble constant is
dr/dt*1/R, it is constant in time. The parameter q is constant at -1.
It is defined as \frac{-\ddot R R}{\dot R^{2}} or
\frac{-\ddot R}{RH^{2}}. Since H is constant in time, \ddot R must
increase with time in proportion to R. So, of course, as with any
exponential, all derivatives are exponential.

Does this mean the acceleration is constant for a given metric
distance?

(Thanks for the study references, by the way.)

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