Universality of the λ ≥ √2 bound in string-theory scalar potentials

Establish whether the lower bound λ ≥ √2 for the slope parameter in the exponential scalar potential V(φ) = V0 e^{-λφ}, as realized in effective single-field models derived from string-theory constructions, holds universally across the asymptotic regions of moduli space under perturbative control.

Background

The paper studies minimally coupled, single-field quintessence with an exponential potential V(φ) = V0 e^{-λφ} and emphasizes the importance of measuring the slope λ from cosmological observations. In string-theory contexts, scalar potentials often take exponential forms, and known examples in asymptotic regions of moduli space suggest a lower bound λ ≥ √2.

The authors reference a conjecture that this bound is universal across string-theory scenarios. Confirming (or refuting) this universality is a theoretical open problem with direct relevance to interpreting cosmological constraints on λ from datasets such as DESI, Planck, and DESY5.