According to physics stackexchange "Exotic matter is matter with negative energy density, or to be more precise, where the energy density tensor trace invariant is negative... If we had exotic matter, we would be able to do much more interesting things than an Alcubierre drive.* We could build wormholes, or time machines...
Wiki says this of exotic matter: "Hypothetical particles which have 'exotic' physical properties that would violate known laws of physics, such as a particle having a negative mass."
* An Alcubierre drive is a way in which a spacecraft could achieve faster than light travel (FTL) if negative mass existed. "Rather than exceeding the speed of light within its local
frame of reference, a spacecraft would traverse distances by contracting
space in front of it and expanding space behind it, resulting in
effective faster-than-light travel....Although there has never been any evidence that such matter exists, some theoretical models (that depart from the Standard Model) require it to exist.
See, the trouble with writing scifi is that one thing leads to another. You wouldn't believe some of the stuff I've discovered since delving into this subject! Remember Casimir forces?