The objects are not accelerating because energy is being directed at them. The space they sit in is expanding. Relative to its nearby surroundings an object isn’t moving any more than usually does. Galaxies can be bound to each other by gravity in their local group. The objects are passengers riding on space, which is expanding. I hope this makes sense.
It helps, but it still begs the question, what energy is causing space itself to expand? And what does that even mean? We talk about the “fabric” of space but of what does “space” itself really consist?