Does this memory foam mattress need a box spring or special foundation?

No flexing box spring is needed, it wants a flat, firm, continuous surface. A platform bed, slats under 3 inches apart, a bunkie board, or an adjustable base all work. The support comes from a 6-inch firm foam core, not springs, so a slatted base with wide gaps can let the foam bow between slats and undermine the firm feel. A solid platform is the simplest way to keep this Sealy Cocoon performing as measured.