Given the universe’s acceleration, could it end in a Big Rip?

We are currently living in a universe in accelerated expansion, which means that objects in the universe recede away from us with a speed that grows with the distance. Even if we waited an infinite amount of time, we would never be able to observe beyond some distance because objects very far away from us are receding away from us so fast that neither light, nor gravitational waves nor any other type of information emitted by those objects would ever be able to reach us.

We know that the expansion of the universe is accelerating, but if the acceleration was itself speeding up, then the size of the observable universe would shrink and there would be a time where the observable universe would be so small that we wouldn’t even be able to see our neighbouring galaxies. When the size of the observable universe is even smaller than the minimal length we can conceive, this would correspond to a Big Rip, possibly tearing apart the whole structure of space and time.