In most literature I have found, research into the Alcubierre Metric, and Warp Drives seems to be highly focused on the plausibility of superluminal travel.
Today I was thinking to myself that maybe we're asking hard questions before easier ones. After all we built sub-sonic planes before we built supersonic ones.
So are there any solutions to the Alcubierre Metric that are focused on sub-luminal travel. Like in the realm of 0.1x-0.5x the speed of light?
I will expand my comment in an answer:
$v$ in Alcubierre is an arbitrary function of time, which can be interpreted as the velocity of the warp drive. In particularly it can lead to arbitrary high acceleration, resulting in arbitrary low round trip times in proper time without experiencing time dilation. The latter is a truly coordinate independent statement, which to me is the core feature of a warp. See this answer for more details: Is observing (superluminal) velocity independent of choice of coordinates for asymptotically flat spacetimes?
In any case yes, you can build a completely subluminal Alcubierre drive by always taking longer proper time than a light ray to perform a round trip, but you will still need negative energy.
