Cosmological Phase Transitions and the Swampland

I consider the Festina Lente Swampland bound and argue taking thermal effects, as for instance occur during reheating, into account significantly strengthens the implications of this bound. I argue that the confinement scale should be higher than a scale proportional to the vacuum energy, while Festina Lente without thermal effects only bounds the confinement scale to be above the Hubble scale. For Higgsing of nonabelian gauge fields, I find that the magnitude of the Higgs mass should be heavier than a bound proportional to the Electroweak scale (or generally the scale set by the Higgs VEV). The measured values of the Higgs in the SM satisfy the bound. A way to avoid the bound being violated during inflation is to have a large number of species becoming light. If one wants the inflationary scale to lie below the species scale in this case, this bounds the inflationary scale to be $\ll {10}^5$ GeV. These bounds have phenomenological implications for BSM physics such as GUTs, suggesting for example a weak or absent gravitational wave signature from the GUT Higgsing phase transition.