Thermal Festina Lente

Abstract

According to the Festina Lente bound, particles charged under a $U(1)$ gauge field cannot be too light. Otherwise, the largest charged black holes of de Sitter space would discharge in a way that leads to a crunching singularity in violation of cosmic censorship. The Festina Lente bound has previously been extended to also include a background of thermal radiation, but where vacuum energy still dominates cosmic evolution, which imposes a maximal temperature $T\leq T_{\max}=(cV/σ)^{1/4}$. We extend this analysis by accounting for thermal enhancement of the discharge process and making the analysis more quantitative. The result is a bound $m\gtrsim\ell (cV/σ)^{1/4}$ on the masses of charged particles. Here, $\ell$ is a term that depends logarithmically on the gauge coupling and particle charge. At weak coupling this leads to a significantly stronger constraint than the $\sqrt{gq}$ scaling of the original Festina Lente bound. As a result, the present vacuum energy requires every particle of charge $10^{-26}\lesssim gq\lesssim e$ to be heavier than $0.03$--$0.2$ eV, provided its gauge boson is lighter than the Hubble scale. An unbroken gauged $B-L$ with Dirac neutrinos gives $m_{ν,{\rm lightest}}\gtrsim10$--$43$ meV for $10^{-29}\lesssim g_{B-L}\lesssim10^{-24}$, in tension with the DESI DR2 limit once $g_{B-L}\gtrsim7\times10^{-28}$. The same limit bounds a neutrino millicharge to $ε_ν\lesssim2\times10^{-27}$. We also revisit the Standard Model effective field theory constraints from the electroweak phase transition. During slow-roll inflation the Standard Model electron violates the bound over the whole range of Hubble rates allowed by the CMB tensor limit and by nucleosynthesis, unless the photon is Higgsed, its coupling is suppressed, or one considers very fine-tuned versions of Higgs inflation.