On $S$-Matrix Exclusion of de Sitter and Naturalness
  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. On one hand, it strengthens
the case for explanations based on new physics not far from the weak scale. At
the same time, it opens up a question, whether instead the hierarchy is imposed
by the $S$-matrix consistency between the Standard Model and gravity.
