It is well known that gravity does distort space. However, his original paper claimed that it would take a lot of matter, and an awful lot of energy (the amount of energy locked into that matter according to E=mc2) to distort spacetime significantly. This is the real reason for Miguel Alcubierre's pessimistic calculations of how much negative energy a warp drive would require. There is hope though. If another force can be directly converted into gravity, that would avoid those extreme energy requirements. String theory predict that gravity and electromagnetism unify in hidden dimensions.
Alcubierre predicted that warp drive would require negative energy. Small amounts of negative energy has been extracted from the vacuum energy using parallel plates extremely close to each other (the Casimir effect). It has been suggested that it would be possible to use the effect practically using thousands of plates. I have a new idea about how to make the effect stronger still. Fit more plate surface into the same volume by curving the plates (curve them all in the same way to keep them parallel).
Weakly manipulated spacetimes
A relatively weak manipulation of spacetime can be used for better launches that is much cheaper than traditional chemical rocket launches. It can also be used for creating artificial gravity in space colonies with very weak gravity, such as hollow asteroid/comet colonies or to create lower gravity in colonies on high-gravity worlds such as Jupiter or as a method of BTC travel. It is possible that simple manipulation of vacuum energy can create a weakly manipulated spacetime (because vacuum is spacetime), in which Casimir effect is not so far-fetched after all (though it will not go faster than light because much of the distortion is inside the device). To prevent the plates from slamming together repulsive magnetic fields or mechanical holding in the edges (which leaves the space between them free). Other possibilities without parallel plates, but still leaving microscopic empty spaces surrounded by matter which creates Casimir effect, is microchannel plates or cylinders inside cylinders. The latter would require many layers, not merely two. Casimir effect only works in vacuum, and enclosing the device into a vacuum chamber would create a push-down effect on the bottom of the vacuum chamber that would nullify the net effect. It can, howewer, be activated on extremely high altitudes with virtual vacuum, after a "first stage" based on aeroplane technology possibly combined with magnetohydrodynamic launches.
I have done an experiment. I suspended an electromagnet from a force meter inside a vacuum chamber. I could measure no effect on apparent weight distinguishable from background vibration when I activated the electromagnet in vacuum without egg shells or with raw egg shells attached to the electromagnet, but with cooked egg shells attached to the electromagnet the apparent weight of the device decreased by 0,05 to 0,1 Newton, while the background vibration was only 0,01 to 0,02 Newton. I concluded that the cooking purged the pores in the egg shells from dirt, allowing them to work as Casimir microchannels. In all experiments except the control without egg shells I used four halves of egg shells and the apparent total weight was about 8 Newton. Others should try repeat the experiment and, if they can afford, use true microchannel plates instead of egg shells (now known as "poor man´s microchannel plates"). If it works, better materiel may create useful manipulation of the vacuum (and of course vacuum energy).
However, when I repeated the experiment the same effect was measured without egg shells, so the error source cannot be ruled out.
Strongly manipulated spacetimes
Although nothing can move faster than the speed of light through spacetime, there is no relativistic constraints on spacetime itself. Strong manipulation of spacetime can therefore be used to create traversable wormholes and Alcubierre-like warp drives. Another note about Alcubierre drive. If the spacetime manipulation is generated by multiple generators, where each generator individually creates a slower than light effect but the collected effect of all the generators is faster than light, that would solve the problem about quantum effects since there would be no fixed event horizon to generate Hawking radiation. Using "anti-gravity" for better launches can also be considered strongly manipulated spacetimes if the launch is from a black hole. Strongly manipulated spacetimes can also be used for preventing the end of the Universe. Recent observations show that the expansion of the universe does not accelerate per volume unit, but that the expansion of the Universe accelerates because there is more and more space that can expand, strengthening the big chill theory and weakening the big rip theory.
Ideas and possibilities
Short electromagnetic waves
Multiple scientific theories, including String Theory, independently predict that gravity and electromagnetism unify in higher dimensions. String theory and others predict that the higher dimensions are hidden because they are extremely small. If an electromagnetic wave is made short enough to fit into the hidden dimensions, it would manipulate space-time efficiently. This is the possibility directly predicted by string theory. The other, highly speculative possibilities have been moved to the talk page.
The engineering problem
Extremely short-waved photons are highly energetic, but it would only be necessary to produce a relatively small number of such photons, because they are very energetic. One way of producing such photons would be to focus a lot of laser energy onto very few atoms (ie a nanoscopic particle), heating them to a extremely hot plasma that would radiate a few ultra-short photons. The Alcubierre metric would require massive manipulation that, if triggered inside the craft, would tear the craft apart. One solution would be to eject nano-particles in controlled trajectories, and then fire lasers at them with perfect timing (ie coordinated by a atomic clock), so that multiple gravity-manipulating effects in a series are simultaneously triggered outside the craft (that is, all nano-particles are hit by laser beams at the same time, but the lasers fire at slightly different times to compensate the distance between the nano-particles). This would, by virtue of producing no discrete event horizon, avoid the problem about Hawking radiation.