Borrowed Tides by Paul Levinson (2001)

An expedition sets off in our near future to visit Alpha Centauri for the first time. The twist: it's a sixteen year round trip, the ship can only carry enough fuel to get there, and getting home depends on a gravitational slingshot thingawhatsit that may or may not work. And, in the grand tradition of these sorts of books, weird things start happening, culminating with the crew's realization, after the slingshot has failed, that they are in fact traveling back to Earth, they're just doing it backward in time.

An interesting concept wrapped in an irretrievably shoddy structure and deeply lazy writing. Which are pretty much the same thing, come to think of it. There really are a few neat ideas here (art with DNA, so it changes with the subject over time) but Levinson lacks both the scientific knowledge and the writerly skill to carry off the hard SF elements (various quantum mechanical things). Having one is usually sufficient and having both is preferable; having neither is just painful. Instead he's slapped a flimsy layer of, I kid you not, Native-American mysticism over top and called it done. In actuality it's silly, and obnoxious because it's silly.

Don't waste your time.