everything that involves wormholes/timetravel/FTL in current science involves something like negative mass, negative gravity, infinite energy or some other exotic resource that, which at this point is really not even close to being able to being tested in any way.
All of those things exist. but we don't know how to make them in significant amounts;
Negative energy (and by extension, mass, if we were to somehow extend the effect) can be created with the Casimir effect.
Dark Energy behaves as negative gravity in some situations.
Infinite energy exists, in a very strange/unconventional way, within every single singularity as they have infinite energy density (but zero area...). We can't interact with it, only the very powerful forces directly "outside" it though.
It's just speculative mathematics based on one of several current theories, which may be accepted as the current best candidates, but are nowhere near proven or even tested.
Everything in science fantasy is pretty far-fetched; assuming some current hypothesis to be justified in such a setting is more than reasonable. Maybe not in real life by any means, but here? Meh.
I'd say were orders of magnitude closer to manipulating gravity now that the higgs field is confirmed, then we are to interstellar travel of any kind. We can now say that with the higgs field established, we may "soon" detect gravitons. and then "soon" thereafter we might be able to manipulate the graviton in the same way we manipulate photons/electrons today.
We have tentatively confirmed the existence of gravitons through analysis of binary pulsars I believe, by measuring the "gravity waves" they emit. I'm not yet an expert in the field, so you'd have to investigate that for yourself
Lot's of ifs and maybes. There is currently no analogy of how to get to negative mass or negative energy that i know off. we don't have negative light or negative electricity for example.
"Negative energy" is actually pretty mundane; gravity behaves as negative energy (that is, an object exposed to kinetic [positive] energy will be pushed away, while something affected by gravity will be attracted towards the source).
Alcubierre drive is one of the more fleshed out options suggested but that still requires a few grams of exotic matter. I also seem to recall it's not possible to interact with the bubble making things like stopping a problem.
If I'm remembering correctly, the main problem with the drive, aside from the negative mass required in the ship, you require 'beacons' also filled with negative mass on the way to your destination.
You know what I do when I face problems with theoretical physics? I get back to studying and working on my degree, while actual scientists work on the problems. I don't think any of us here can give an informed opinion on the subject.