For a model universe with the scalefactor 'a', if a(dot)/a=constant, is that called an accelerating universe?

(where the dot is a time derivative)

Could it not be that our universe has always had a(dot)/a = constant, everywhere and at all times?

In such a universe would the Hubble parameter be H(z)=constant or H(z)=(1+z)*constant?

Thankyou.