A body thrown up, stalling and falling back in Earth’s gravitational field accelerates towards Earth. No new energy is created, it is potential energy converted into kinetic energy.
Space expansion accelerating seems to be not quite analogical. Where is the potential energy converting to kinetic energy expanding space? Is space falling back to where it started father out? It seems that space expanding is more analogical to a ball being thrown into the air, out it goes. Muscle potential energy sends the ball on its way. What potential energy has that effect on space? Is space in rebound mode, expanding outward, like a compressed spring? If potential energy does not account for expanding space, then could it be energy is being added to the universe resulting in space expanding? The expansion is accelerating constantly, so that would seem to require a constant addition of energy. But if our universe is self contained, there is no external source of energy to create a force to accelerate space.
These considerations suggest that so called accelerating space might instead be space expanding inertially, like a rocket gliding after fuel has run out. Suppose space plus (light) motion is 4 dimensions and empty space is 3 dimensions. Then an unchanging (invariant) ratio of dimensions, 4 : 3, would nor require adding energy to the universe. Three dimensional space would grow radially by 4/3 L when 4 dimensions grow by L.
Where does the energy for DE come from?