Although to go back in time properly, you still need infinite energy.
Or rather, to move normal, positive mass through space faster than light, you need infinite energy.
If mass could have imaginary values (square root of -1 kind of imaginary) then it would take infinite energy to make it go SLOWER than lightspeed. Those particles are the slightly famous Tachyons from sci-fi like the Tachyon Transmitter for FTL communication systems.
If you could have mass with negative values, you could make a stable wormhole. Then just use relativity to speed up one opening close to lightspeed for a while, and the 2 ends desync temporally, and thus you can go backwards in time through the wormhole.
If you could move a patch of space faster than light, with positive mass sitting inside it at rest, then you could move mass from point A to point B faster than light. (Alcubierre warp drive)