Revisiting the scalar weak gravity conjecture

We revisit the scalar weak gravity conjecture and investigate the possibility to impose that scalar interactions dominate over gravitational ones. More precisely, we look for consequences of assuming that, for leading scalar interactions, the corresponding gravitational contribution is sub-dominant in the non-relativistic limit. For a single massive scalar particle, this leads us to compare four-point self-interactions in different type of potentials. For axion-like particles, we retrieve the result of the axion weak gravity conjecture: the decay constant f is bounded by the Planck mass, f<MPl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f < {M_{Pl}}$$\end{document}. Similar bounds are obtained for exponential potentials. For quartic, power law and Starobinsky potentials, we exclude large trans-Planckian field excursions. We then discuss the case of moduli that determine the scalars masses. We retrieve the exponential dependence as requested by the Swampland distance conjecture. We also find extremal state masses with field dependence that reproduces both the Kaluza-Klein and winding modes behaviour. In particular cases, our constraints can be put in the form of the Refined de Sitter Conjecture.