If I understand this correctly, you're talking about something similar to Star Trek's Warp Drive (or the Alcubierre drive, for something less fictional). Instead of stars and galaxies moving at the speed of light, the space around them expands and the expansion accelerates at a rate that will eventually make the speed of expansion larger than the speed of light. Or in other words, stars and galaxies will continue to move at their sub-luminar speed, but the space in which they exist will expand so fast that the expansion will cause the distance between them to increase at such a rate that light will not be able to keep up.

[Edit: and, er, all that has something to do with dark energy?]

OK, but in that case, and if we still exist as a technological civilisation at that time (very doubtful) we might be able to use the effect for our own benefit. By building warp drives and er, not-quite-travelling faster than light, by expanding space around a ship, etc.