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 Lambdainfmax ~ 109 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, sqrtxi ~ 1016 GeV. At the same time, the TCC results in an upper bound on the corresponding gauge coupling constant of gmax ~ 10-14. We are able to show that this constraint translates into an upper bound on the gravitino mass of m3/2max ~ 10 MeV, which opens the possibility that dark matter is accounted for by thermally produced gravitinos, if the reheating temperature is close to Treh ~ 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.
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