If the universe expands at faster than the speed of light, does it begin to go back in time?

We looked at accelerating expansion in the most recent question of the Strange Universe series. Obviously, if expansion constantly accelerates, it will exceed the speed of light. Observation indicates it already has, so does that cause time dilation?

This is a continuation in the Strange Universe series.
1—What is the expanding universe expanding into?
2—Big Bang Theory—How can you divide infinity into a single finite whole?
3—How would you answer this speed-of-light question?
4—What happens when the expansion of the Universe reaches the speed of light?
5—What’s your Strange Universe example to illustrate Sir Arthur Eddington’s quote?