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Answer by Joshua Engel:
The cream doesn’t become denser, but it does become less fluid. That is, the same amount of mass occupies more space, so the density goes down, but it flows much more slowly (“more viscous”).
Whipped cream is a colloid. Microscopic bits of air are incorporated into cream, surrounded by thin sheets of milk fat. The fats are long molecules that can cling to each other, forming a tiny bubble that traps the air.
These bubble surfaces have much less freedom to move. The molecules support each other, preventing them from moving. So the whipped cream flows more slowly than the same amount of cream without the air bubbles in it. It weighs exactly the same as it did without the air (or maybe slightly heavier when you count the air, but that’s a tiny, tiny mass), but the volume is considerably larger, so the density is much lower.
You can see a similar effect in soap foams.
The soap and water are liquid. But when you whip air into it, the surface tension prevents them from moving much, and the result doesn’t flow.
Mayonnaise and other kitchen emulsions follow similar rules. Mayonnaise is made of (liquid) oil and (liquid) acid (such as vinegar or lemon juice). Here, microscopic droplets of the oil are covered in a thin layer of the acid. The acid keeps the droplets in place, while the droplets prevent the acid from flowing freely. The combination is stiffer than either the acid or the oil separately.