Trans-Planckian Censorship and Inflation in Grand Unified Theories

TL;DR

This paper explores how the trans-Planckian censorship conjecture constrains inflation models within supersymmetric grand unification, particularly D-term hybrid inflation, leading to specific bounds on parameters like the gravitino mass and implications for dark matter.

Contribution

It demonstrates that D-term hybrid inflation can satisfy TCC constraints and derives bounds on gauge coupling and gravitino mass, linking inflation, supersymmetry, and dark matter.

Findings

TCC constrains inflation energy scale to below 10^9 GeV.

Upper bound on gravitino mass is approximately 10 MeV.

Dark matter could be thermally produced gravitinos near 100 TeV reheating temperature.

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.