For the past 10 billion years a linear expansion was a pretty decent approximation. The early universe slowed its expansion, which makes the relative reach of the ant even larger (or, equivalently, the early recession speeds were larger).

The Hubble rate is still decreasing. It's expected to approach a constant in the future. I covered that in the second paragraph:

> In the distant future, in a universe completely dominated by dark energy, your statement will be right.