On $S$-Matrix Exclusion of de Sitter and Naturalness

Understand

The cosmological constant puzzle, traditionally viewed as a naturalness problem, is evidently nullified by the $S$-matrix formulation of quantum gravity/string theory.

• We point out an implication of this fact for another naturalness puzzle, the Hierarchy Problem between the weak and Planck scales.
• By eliminating the landscape of de Sitter vacua and eternal inflation, the $S$-matrix formulation exhibits an obvious tension with the explanations based on anthropic selection or cosmological relaxation of the Higgs mass.
• This sharpens the Hierarchy Problem in a profound way.