Trans-Planckian Censorship and Inflation in Grand Unified Theories

Abstract: The recently proposed trans-Planckian censorship conjecture (TCC) amounts to the claim that inflation models with an inflationary energy scale larger than Lambda_inf^max ~ 10^9 GeV belong to the swampland, i.e., cannot be embedded into a consistent theory of quantum gravity. In this paper, we point out that this constraint can be readily satisfied in D-term hybrid inflation (DHI), which is a well-motivated inflation scenario in the context of supersymmetric grand unification. In DHI, the amplitude of the primordial scalar power spectrum originates from a Fayet-Iliopoulos term of the order of the unification scale, sqrt{xi} ~ 10^16 GeV. At the same time, the TCC results in an upper bound on the corresponding gauge coupling constant of g_max ~ 10^-14. We are able to show that this constraint translates into an upper bound on the gravitino mass of m_3/2^max ~ 10 MeV, which opens the possibility that dark matter is accounted for by thermally produced gravitinos, if the reheating temperature is close to T_reh ~ 100 TeV. Interestingly enough, a somewhat similar gravitino mass range has recently been derived in a model that aims at explaining dark energy in terms of axion quintessence and resolving the Hubble tension by means of decaying gravitino dark matter.