Refined de Sitter Conjecture (RdSC)

Establish whether every four-dimensional quantum-gravity effective theory of the form S4d with positive scalar potential V must satisfy at every point in field space either a lower bound on the normalized gradient of the potential, M_p^{-1}||∇V||/V ≥ c, or an upper bound on the minimal normalized Hessian eigenvalue, M_p^{-2} min_eig(M) / V ≤ −c′, for some positive constants c and c′ of order one.

Background

The refined de Sitter conjecture (RdSC) is a response to tensions between the original de Sitter swampland conjecture and known features of the Standard Model sector (e.g., the Higgs and QCD potentials).

In this review, the authors present the RdSC as applying to four-dimensional effective theories derived from string theory (or quantum gravity) with action of the type S4d and V>0, and they discuss tests and implications, including constraints for inflation and late-time cosmology.

The conjecture is formulated as a disjunctive condition on the potential’s slope or curvature, and is widely used as a theoretical prior in model building; however, it remains unproven.