I think that Warp Drive based propulsion systems are very possible. If you get away from the paradox of traveling faster than light creating some tunnel through time that will take you into the past, you will understand that Warp Drive is really nothing more than travelling very fast and occupying more space at any one time.
Before our Universe was filled with solar and celestial gravity based on mass in the form of stars, black holes and planets, there really wasn't any large amounts of matter in the Universe that created gravity on the scale that we see it today. Maybe there was a lot of Pre-Big Bang dust or particles of Pre-Big Bang matter, but nothing on the scale of a black hole or planet.
Without matter creating mass and gravity through very large planetary bodies, which if you think about it, stars planets and even large chunks of rock and ice are all similar to black holes. Similar to black holes in so much that each celestial object creates a pull on another object. Some objects are able to escape the gravity of a celestial object while other are not.
The real trick in Warp Drive capable ships is the ability to reduce the amount of particle mass that the ship encounters the faster that the ship travels to light speed.
Think of it this way. You have a 300 meter field. You are at one end, the finish line is at the other. You have a consistent field of pebbles, representing gravity, raining down every yard. As you start to walk, you can feel the pebbles hitting your body. The slower that you walk means that your body encounters more pebbles based on how wide and thick you are. But as you walk faster and faster towards the end of the field, you are pelted with more and more pebbles causing you to slow down.
Therefore,traveling faster and faster to the light of speed will see more gravity encountered on a micro scale based on micro elements that are electromagnetically attracted to your ship. Elements that are attracted would add more mass to the ship over, time slowing it down as more energy was needed to pump into the engines to overcome the increased mass. Basically like the barnacles that collect on a ship that causes increased weight that slows the ship down have to be cleaned off periodically.
If the field around a ship can break the electric and magnetic bounds between the elements that interact with the field, then less mass is added to the ship allowing it to travel faster and faster. At some point the ship could reach a peak velocity and turn its engines off to conserve fuel while gliding through space. As long as the field that disrupts the electric and magnetic bonds in an atom remain stable, the ship should be able to glide indefinitely through the small region of space that has been created that is now similar to space-time before the Big Bang.
But the energy needed to create Warp Drive would need to be near infinite you say. That might be true.
But as the ship travels faster and faster through space-time the energy created by the ship moving through space-time could be siphoned from around it to add back into the propulsion system to keep the ship's energy stores at nearly an infinite amount of energy or an amount of energy filling the ships energy stores at the speed of light.
