A frame of reference is relative. Just a comparison to another system. It is not a physical thing. It is a physical system, be it thermodynamic, relativistic, quantum, non/inertial, whatever. A lot of folks just assume that when frames of reference are talked about, that it must be inertial.
Not necessarily inertial, but beware that inertial or not can be told locally without any outside reference, a simple accelerometer would suffice. So inertial frames are special. In an absolute sense.
.../... Thankfully because acceleration is relative, an observer outside of your frame of reference will see your virtual particles become real. That doesn't help us either, but the methodology is key. As you know, frames of reference are relative.
Inertial frames are relative, as proper time/distance transforms can translate observables of one frame into observables in the other. Well, I guess taking acceleration into account that is also possible for accelerated frames (introducing Coriolis "forces" for instance).
So I flipped it. How about this: We live in an accelerating universe. Our universe is accelerating at rates which we cannot ever hope to achieve. Furthermore, the rate of expansion is a curve, meaning galaxies further away are flying apart faster than the ones flying apart closer to us. Neat. So from the point of view of the universe, which is the accelerating frame of reference, our emdrive is accelerating slowly, compared to say the CMB frame of reference.
It's not clear what time derivative you are talking about : the rate of expansion (Hubble "constant") that goes as ~2.3e-12(m/s)/m (hey, it has dimension of a frequency !), or the change of this rate, which right now seems to be decelerating ( for a given distance you will see slower receding objects crossing this distance in the near future ) in spite of the mysterious acceleration of expansion (expansion not slowing as fast as it should, but still slowing from usual mass content gravity) ?
More confusing : the universe isn't locally accelerating, makes no sense, its local content has a local average speed that can be used as a local inertial frame of reference, but it is not accelerating in any absolute sense, there is nowhere special toward where it could accelerate ! The CMB is part of the content, take or give a few 100s km/s it's the same local inertial frame as the stars and gas averaged on a decently sized local patch, it goes with the flow, and this flow is 0 relative to receding neighbouring patches all around. Local universe is not accelerating if seen at coarse graining bigger than anisotropies. What particular direction of the sky the CMB is supposed to be accelerating (I'm not speaking of our galaxy relative velocity with CMB) ? And even if it were, it would just be free falling with us (say, with the local cluster) at the same acceleration toward a big lump in the neighborhood. Anyway it's not accelerating relative to us and relativity makes no difference between free-falling and inertial velocity in nothingness.
So lets imagine ourselves on a spaceship in Earth orbit and you are equipped with our brand new emdrive technology. From your frame of reference you are barely moving compared to the accelerating speed of universal expansion happening around you.
I'm barely moving relative to the speed of a specific cluster 1Bly away but in the walls of my ship, or even when considering the whole galaxy, the Universe could be static rather than expending wouldn't change a thing for me, how could a phenomenon occurring over cosmological times/distances could make any difference locally ?
So imagine yourself inside your space ship and you're looking intently at your prototype emdrive looking for real particles to appear out of the qv fluctuations, you don't see them. Now imagine the universe is the observer. The universe observing your emdrive would see some virtual particles from the qv becoming real. This only works if the universe is expanding.
What part of the universe is observing, my local patch average ? A co-orbiting inertial frame ? Earth ? Sun ? Galaxy ? None of those scales make any care of the fact that universe is expending, or that the rate of expansion varies a bit in a long while (sorry, can't find precise numbers here, but next to impossible to measure inside a lab, so making no difference for a ship).
So with this mechanism, you get some arbitrary flux of real particles from the qv frame of reference (I'm assuming the qv and its randomly produced particle pairs are not inertially related to our inertial frame of reference) popping into your local frame of reference (as observed from the point of view of the universe). So I'm picturing the pair production happening randomly, becoming real, and immediately flying away at a rate matching the speed and direction of the expansion of the universe minus the influence of gravity, isotropically. My head hurts.
I believe so. Trying hard and seriously to get your point but "matching the speed and direction" in one hand and "isotropically" the other seems like an oxymoron. Looks like your are longing for the inflation epoch when
a field of accelerated expansion (second order) was so strong it could everywhere rip apart virtual particles pairs to make them real. Would be compatible with the isotropy. Thing is, when such a field is so strong, reality tends to be not very stable and quickly evolves. We are in a stable epoch, stability of time prevents energy conservation breaking (as would be the case when virtual particles become real, note that the accelerating field is actually decaying, it loses some punch in the process). And stability of space (isotropy) prevents momentum conservation breaking. As per Noether's theorem.
.../... Is gravity keeping the expansion of the universe in check at small scales? .../...
Yes. Expansion observed now is just an inertial collective movement from initial expanding conditions. Gravitationally bound objects are not obliged to abide to Hubble law. The dark energy or lambda parameter on the other hand is supposed to act on metrics by "fabricating" more space between objects (while a relative inertial receding velocity don't really make more space per se), so if its pressure increases it could conceivably first alter then rip apart gravitationally bound objects. Local effects (at galaxy scale) are not expected to occur soon.
I think the logic above would have us all awash in real particles all the time. Maybe that's where matter comes from, lol.
Some think this is exactly what happened but not all the time, just at the end of the inflation when the inflaton field decayed into usual particles, and thus stopping inflation, see, this process can't last long. It's not stable.
Can't give other opinion for the rest as the Unruh effect is above my head, also I would tend to agree that resonance seems pointless (except maybe for efficiency of the coupling to the RF generator as the system must be analysed as a whole).