Supercritical string cosmology drains the swampland

The first and second swampland conjectures (FSC & SSC) are substantially modified in noncritical string cosmology, in which cosmic time is identified with the timelike Liouville mode of the supercritical string. In this scenario the Friedmann equation receives additional contributions due to the noncriticality of the string. These are potentially important when one seeks to apply the Bousso bound for the entropy of states that may become light as the dilaton takes on trans-Planckian values, as in a de Sitter phase, and restore consistency with the FSC and in at least some cases also the SSC. The weak gravity conjecture (WGC) for scalar potentials is saturated in the supercritical string scenarios discussed in this work, but only if one uses the dilaton as appears in the string effective action, with a kinetic term that is not canonically normalized. In the case of a noncritical Starobinsky potential, the WGC is satisfied by both the canonically normalized dilaton and the dilaton used in the string effective action.