You know. To get ones head around the way the Hubble constant is thought to work with a universe is tricky. In the simplest representation is can be seen as a linear function, sort of, depending on how we define the density of a universe, dark energy, GR, etc etc. but

It still seems to be accelerating, although very slowly. Try this one.

"The Hubble parameter measures the relative speed of the scale factor a(t) of the universe, formally H(t) = [da(t)/dt]/a(t). It comes form the FLRW metric and is a function of universal cosmological time; its value is determined by the mass/energy content of universe by the first Friedman equation (obtained by the Einstein's field equations) H^2(t) = (8piG/3) x ϱ(t) - kc^2/a^2, where ϱ = ϱ_m + ϱ_d + ϱ_r is the total mass/energy density given by matter (luminous and dark), dark energy and radiation; k is the curvature parameter.

The value of the Hubble parameter *now* is called Hubble's constant.

Since it is possible to define a well precise relationship between time and redshift z, they measure the same thing and H can be expressed as a function of z. Now, the various densities decrease as the scale factor increases. The key point is that they have *different* dependencies on the scale factor: ϱ_m ~ a^-3, ϱ_r ~ a^-4 and ϱ_d ~ constant.

This implies that at early times (ie small a(t)) the radiation was the dominant component and the expansion speed, and therefore H, had a different value from now, then matter started to dominate since is decreasing more slowly than radiation and again speed changed. At some point in the past, the third component, the dark energy, started to dominate since matter was more and more diluted by the expansion (the most recent data seem to indicate around 5 billion ago). Since ϱ_d stays constant during the expansion (this *the feature* of dark energy, together with its negative pressure (!) ), the speed *increases* with time, that is the universe accelerates expansion. Apparently, we are living now in a dark energy-dominated universe. " By Emanuele Fiandrini · INFN - Istituto Nazionale di Fisica Nucleare

Then look at how cosmologists define a

Comoving distance. "Comoving distance and proper distance are defined to be equal at the present time; therefore, the ratio of proper distance to comoving distance now is 1."

Finally look at

Value of the Hubble parameter over time from Stackexchange

Think Emanuele's presentation is the one easiest to follow myself, but I think we still can use it as a 'linear representation'?