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

## TL;DR

This paper demonstrates that in quasi de Sitter backgrounds, the scalar weak gravity conjecture naturally follows from the swampland distance conjecture and the covariant entropy bound, suggesting strong constraints on scalar potentials in effective theories.

## Contribution

It establishes a connection between the scalar weak gravity conjecture and the swampland distance conjecture, highlighting potential constraints on scalar field potentials beyond existing de Sitter conjectures.

## Key findings

- sWGC follows from the swampland distance conjecture in quasi de Sitter space
- Potential shapes of scalar fields are highly constrained by the distance conjecture
- The paper clarifies previous misconceptions about cosmological implications of the sWGC

## Abstract

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.