Bumping into the species scale with the scalar potential

As a quantum gravity cut-off, the species scale ${\mathrm{\Lambda }}_s$ gets naturally compared to the energy scale of a scalar potential $V$ in an EFT. In this note, we compare the species scale, its rate $\mathrm{\mid }\mathrm{\nabla }{\mathrm{\Lambda }}_s\mathrm{\mid }\mathrm{/}{\mathrm{\Lambda }}_s$ and their field dependence, to those of a scalar potential. To that end, we first identify a string compactification leading to a scalar potential with the same properties as the species scale, namely, being positive, starting at a maximum in the bulk of field space and going asymptotically to zero. The trajectory followed in our 14-fields scalar potential is the steepest descent. Evaluating the rate $\mathrm{\mid }\mathrm{\nabla }V\mathrm{\mid }\mathrm{/}V$ along this path, we then observe a local maximum, or bump, a feature noticed as well for the species scale. We investigate the origin of this bump for the scalar potential, and compare it to that of the species scale.