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

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 $η$ problem and the compatibility with the recent ACT or SPT data. The one relies on the choice of a shift-symmetric Kähler potential for the inflaton which revitalizes the SUSY predictions of smFHI, whereas the other employs a Kähler potential associated with an hyperbolic Kähler 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.

💡 Research Summary

The authors present a comprehensive study of smooth F‑term hybrid inflation (smFHI) embedded in two distinct supergravity (SUGRA) frameworks, aiming to resolve the long‑standing η‑problem and to bring the model into agreement with the latest CMB measurements from ACT, SPT, and Planck. The first framework, “shift‑symmetric SUGRA” (shSUGRA), employs a Kähler potential of the form (K_I=-\frac12\hat Z(S-S^\ast)^2), which protects the inflaton’s real component against large SUGRA corrections through a continuous shift symmetry. The second, “N‑dependent SUGRA” (NSUGRA), uses a hyperbolic Kähler potential (K_I=N m_P^2\ln!\bigl(1+\hat Z|S|^2/(Nm_P^2)\bigr)) with (N<0), providing a non‑compact moduli space that naturally yields a small positive contribution to the η‑parameter.

Both constructions introduce a decoupled heavy modulus field (h) that appears only in the Kähler sector, with (\hat Z=(f+\bar f)^\alpha) and (\hat K=\beta m_P^2\ln(f+\bar f)). By fixing (\langle f\rangle=1/2) the authors set (\langle\hat Z\rangle=1) and (\langle\hat K\rangle=0), ensuring canonical kinetic terms for the inflaton while keeping the modulus stabilized throughout inflation. This setup is motivated by string‑ and D‑brane models and avoids the need for additional superpotential terms for (h).

The superpotential accommodates two classes of smFHI: (I) (W=S,M^{2}\bigl