GUT-Scale Smooth Hybrid Inflation with a Stabilized Modulus in Light of ACT and SPT Data

Abstract: We analyze a generalized framework of smooth F-term hybrid inflation (smFHI) consistent with gauge coupling unification within the Minimal Supersymmetric Standard Model (MSSM). The embedding of the model in two specific Supergravity settings addresses at the same time the $\eta$ problem and the compatibility with the recent ACT or SPT data. The one relies on the choice of a shift-symmetric K\"ahler potential for the inflaton which revitalizes the SUSY predictions of smFHI, whereas the other employs a K\"ahler potential associated with an hyperbolic K\"ahler manifold. An essential role in both our constructions is played by a decoupled superheavy field without superpotential and Kaehler potential inspired by string- and D-brane--based models. Our proposal can be realized for a variety of representations for the Higgs fields involved in smFHI and assures monotonic inflationary potential.