In PoW consensus, if a miner could solve the puzzle, they receive some monetary reward (some coins) to incentive miners, since mining process has a considerable monetary cost for miners including providing hardware and energy/electricity cost.
However, in PoS, participation in transactions validation has not a significant monetary cost for validators (i.e. stakeholders) (I hope I am right), and if so, is there any incentive to motivate stakeholders for participating in transactions validation?
Also, what is the penalty of a validator who ex. confirm a double-spent transaction?