Relating the scalar weak gravity conjecture and the swampland distance conjecture for an accelerating universe

For any quasi de Sitter background, we show that a recently proposed scalar weak gravity conjecture (sWGC) follows from the swampland distance conjecture, together with the covariant entropy bound. While pointing out the limitations of our argument, we suggest how further generalizations of our result might indicate that the shape of the potential of a scalar field in a low-energy effective field theory gets highly constrained due to the distance conjecture alone, going beyond the refined de Sitter conjecture. We also correct some previous comments regarding cosmological implications of the sWGC.