de Sitter conjecture

What the term means here

The proposal that scalar potentials in any consistent quantum-gravity effective theory satisfy a gradient bound of the form |∇V| ≥ c·V, with c a positive number of order one in Planck units. Taken at face value it forbids stable de Sitter minima, where the gradient vanishes and V is positive.

Why it matters to this question

It converts a hard construction problem into a sharp, falsifiable-looking criterion, and it is the single statement around which the post-2018 debate organizes.

What this does not establish

The conjecture rests on asymptotic and thermodynamic arguments, not on a ten-dimensional proof. Critics argue that an order-one c is in tension with slow-roll inflation and with the observed value of Λ, and that the conjecture over-generalizes tree-level no-go theorems.