The Alcubierre drive was theorized by Mexican physicist Miguel Alcubierre in 1994. The hypothetical warp drive envisioned that a spacecraft could achieve faster than light speed travel, basically warp factor 5 and beyond. In the Alcubierre theory, a spacecraft would traverse emmense distances by contracting space ahead of it and expanding space behind it which in effect would create a vortex in which a vessel could travel faster than light.
The theoretical Alcubierre drive would require a hull of exotic matter to transport passengers at super light speed and hence travel through spacetime. The proposed Alcubierre drive calls for a negative energy density which requires exotic matter that is also theoretical, it's existence is only theorized and not proven. So if this exotic matter can not be located, or does not exist, then the theoretical spacetime warp drive could never be constructed.
More recently, 2017, two physicists, David Tsang [University of Maryland] and Ben Tippet [University of British Columbia] published a paper in 'Classical and Quantum Gravity'. They believe that they have devised a mathematical model for a theoretical time machine. This time machine they claim is a vessel, in this case a box, that can be moved through time in either direction forward and back. They dubbed their theory Traversable Acausal Retrograde Domains in Space-time [TARDIS].
The methodology they propose is similar to that proposed by Alcubierre. They speculate that the curvature of space-time in the Universe can be used to bend time into a circle for passengers sitting in their envisioned box. Once within the circle travel to all points past and future are possible.
If this bubble/ vessel/ box attains greater than light speed which is mathematically possible as per the thesis, travel through time [spacetime] would be possible. Although it is mathematically possible, at present it is still not feasible to construct this device because the material necessary - exotic matter has yet to be discovered, we are not certain if it does exist.