recovering a result already conjectured from other arguments. The conjecture has far reaching consequences and applies to several interesting physical systems: i) Among chaotic inflation potentials only those asymptotically linear may survive. ii) If applied to the radion of the circle compactification of the Standard Model to 3D with Dirac neutrinos, the constraint implies that the 4D cosmological constant scale must be larger than the mass of the lightest neutrino, which must be in normal hierarchy. It also puts a constraint on the EW scale, potentially explaining the hierarchy problem. This recovers and improves results already obtained by applying the AdS swampland conjecture, but in a way which is independent from UV physics. iii) It also constraints simplest moduli fixing string models. The simplest KKLT model is compatible with the constraints but the latter may be relevant for some choices of parameters.

A Scalar Weak Gravity Conjecture
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The Weak Gravity Conjecture (WGC) was first formulated in [@swampland; @WGC; @distance], see [@review] for a recent review and more references. The most widely studied WGC example is the case of a $U(1)$ gauge boson coupled to gravity. It states that there must always exist a charged particle with mass m and 