"If time travel into the past were possible we would be over-run with tourists from the future." I think Hawking said it, or possibly someone earlier.
Time travel into the future is manifestly possible; we are all doing it at a rate of one second per second. Seems dubious that the rate can be accelerated.
--Boris
Any round trip taken at speeds close to the speed of light will accelerate your travel into the future, without violating any known physical laws, and without requiring infinite energy.