You shouldn't be able to damage a concrete floor by jumping up and down on it.
There will be sound transmission (as you've noticed) and there might be some movement in the floor if it's not properly tied into the walls. This would be more likely with a wooden floor supported by joists as there is more natural movement in wood than concrete.
If there is movement this could cause the ceiling in the room below to show cracks in the plaster (assuming it is plastered) but these aren't structural and shouldn't worry you unduly. If cracks do appear then monitor them to see if they are growing or not. If they don't change length or width then you'll be able to fill them in and repaint. If they do change length or width then it could indicated that there is something amiss - usually something is loose, but this is unlikely with a concrete floor.