I have to add that warp drive belongs in the realm of fantastic science fiction, that is the nonhard variety. In the Trek timeline I can see the Warp Drive being invented by Zepham Cochrain in 2063 or whenever, but I don't really expect the ability to distort the fabric of space-time with gravity and anti-gravity to come all that readily.
An antigravity field would have its own implications, you know how gravity slows down time, well antigravity speeds it up or should do so if it behaves anything like gravity but with the - sign switched with a +.