Complexity equals anything can grow forever in de Sitter space

Recent developments in anti–de Sitter holography point towards the association of an infinite class of covariant objects, the simplest one being codimension-one extremal volumes, with quantum computational complexity in the microscopic description. One of the defining features of these gravitational complexity proposals is describing the persistent growth of black hole interior in classical gravity. It is tempting to assume that the gravitational complexity proposals apply also to gravity outside their native anti–de Sitter setting in which case they may reveal new truths about these cases with much less understood microscopics. Recent first steps in this direction in de Sitter static patch demonstrated a very different behavior from anti–de Sitter holography deemed hyperfast growth; diverging complexification rate after a finite time. We show that this feature is not a necessity and among gravitational complexity proposals there are ones, that predict linear or exponential late-time growth behaviors for complexity in de Sitter static patches persisting classically forever.