Strong de Sitter Conjecture (SdSC)

Prove that, in any field-space asymptotic limit, every four-dimensional quantum-gravity effective theory of the form S4d with positive scalar potential V must satisfy the asymptotic slope bound M_p^{-1}||∇V||/V ≥ √2.

Background

Motivated by the Trans-Planckian Censorship Conjecture and by dimensional-reduction arguments, the Strong de Sitter Conjecture (SdSC) restricts positive potentials only in field-space asymptotics.

The review emphasizes that, although no counterexample is known and numerous top-down tests are consistent with SdSC, it remains a conjecture; it plays a central role for asymptotic quintessence and inflation constraints.