If I remember correctly, acceleration curves spacetime in the same/similar way to gravitation, if the entire universe is accelerating, then it must be accelerating through spacetime to create the effect we know as gravity, so the universe must be a construct that moves through an external fabric of spacetime which is infinite/loops back on itself. If the fabric were to move with the universe, there would be no relative motion so no gravitational effect.
Perhaps the FE universe travels around a torus of spacetime??