Why isn't energy required for the passenger molecule to be carried across the cell membrane by the carrier molecules?

Energy is not required for the passenger molecule to be carried across the cell membrane by the carrier molecule simply because they are moving down a concentration gradient, that is to say movement is from an area of high concentration to an area of low concentration.

When particle move from areas of high concentration to areas of low concentration, they do not need energy. For example this is how the aroma of cooking spreads from the kitchen (higher concentration) to all the other rooms in the house.