Inflation, in my limited understanding, has two implications. The exponential expansion that I have heard referred to as the Inflationary Epoch, and the accelerating expansion sometimes mentioned as a push caused by dark energy. These two implications are part of the explanation of why we can't detect the edge of the universe, expansion looks the same in all directions.

The vacuum energy (negative pressure) working on the expanding universe plays a role in our inability to detect the edge as mentioned in that post and plays the same role as dark energy. Vacuum energy works from beyond and surrounding the expanding universe while dark energy is supposed to be pushing from within the expanding universe. I like the vacuum energy idea better than the dark energy idea. I suggested how vacuum energy might work in my post about vacuum energy density.