Swampland Constraints on the Particle Spectrum with Positive Vacuum Energy

The Swampland approach to quantum gravity research aims to identify the universal features that quantum gravity may have in low-energy physics. One of the most well-known statements, the Weak Gravity Conjecture (WGC), claims that in any consistent quantum theory of gravity with long-range electromagnetic interactions, there is a particle whose mass is larger than its charge in Planck units. This is supported by evidence coming from string theory compactifications, as well as universal black hole arguments. Repeating these arguments in the context of models with positive vacuum energy, such as de Sitter space, one arrives to a second bound on the spectrum: the Festina Lente (FL) bound, which implies a lower bound on the mass of every charged particle.  I will present this bound, derivation, and phenomenological implications for particle physics, models of de Sitter space in string theory, and inflation. Some of these phenomenological implications include bounds in the shape of the Higgs potential, spectrum of milli-charged dark matter, constraints on the matter sector during inflation, and implications for the electroweak hierarchy and comsological hierarchy problems.