The expansion of the universe has always come down to one question for me. In an expanding universe when you throw a ball up what speed does it come down?
My very limited understanding of the topic is that for a gravitationally bound system like the Earth, the usual rules apply, but on cosmological scales the expansion of the universe means that time-translation is not invariant and thus conservation of energy is not well-defined.
Getting rid of the time side then, think of it as an orbit. If the universe was expanding then something could be orbiting slower than gravity would allow. Basically this question keeps bringing me back to the ties between mass and the expansion of the universe. No matter how you look at it mass must be special when it comes to expansion because it is either giving off 'free' energy in the form of slow orbits and acceleration between two objects or it -isn't- giving off that energy and something is canceling it out. Following this rabbit-hole is pretty interesting at a minimum.
if you throw less than escape velocity, about the energy you threw with less system losses. if you throw greater than escape velocity, about any energy is possible less system losses, if you allow enough time for it to come back after its trip around the solar system. if you throw it into the milky way, same thing, easier potentials. if you throw it at relativistic velocities, expansion of the universe could play a significant role.