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

TL;DR

The paper develops two realizations of smooth F-term hybrid inflation (smFHI) embedded in the MSSM with GUT-scale Higgs dynamics, addressing the η problem via a stabilized modulus and two SUGRA frameworks: shift-symmetric (shSUGRA) and hyperbolic (NSUGRA) Kahler potentials. A decoupled superheavy modulus and gauge-unification constraints yield a monotonic inflationary potential V_I without relying on radiative slopes, producing robust predictions for the spectral index n_s and negligible tensor modes. The results show that shSUGRA can be compatible with ACT-SPT data, while NSUGRA—through c_{2K} = 0 and tuned N, α, β—can accommodate ACT-LB-BK18, with mSUGRA excluded at GUT scales; the framework also fixes Higgs vevs at the GUT scale, reducing parameter space and enhancing predictivity. Overall, the work demonstrates a viable path to GUT-scale smFHI that aligns with current CMB constraints while maintaining a monotonic, controlled inflationary dynamics.

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 $η$ 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.

Figures (4)

• Figure 1: Values of $n_{\rm s}$ allowed by Eqs. (\ref{['nhi']}), (\ref{['prob']}) and (\ref{['Mgut']}) versus $\alpha$ for smFHI-I, $\beta=-1$ or $-2$ and $p=2,3$ and $4$ -- the marginalized joint $68\%$ [$95\%$] c.l. regions from P-ACT-LB-BK18 data are depicted by the dark [light] shaded contours (left plot). Resulting values of $(-N_{0})$ versus $M$ for the same $\beta$ and $p$ (right plot). Shown is also the applied color coding in both plots for the various $\beta$ and $p$ values in the legend of the right plot.
• Figure 2: The same as in Fig. \ref{['fig1']} but for smFHI-II and $q=3,5$ and $7$ (instead of $p$).
• Figure 3: Values of $n_{\rm s}$, allowed by Eqs. (\ref{['nhi']}), (\ref{['prob']}) and (\ref{['Mgut']}), versus $a_{\rm s}$ for NSUGRA and smFHI-I [smFHI-II] (left [right] plot) corresponding to the parameter choices discussed in Fig. \ref{['fig1']} [Fig. \ref{['fig2']}]. The marginalized joint 68% [95%] c.l. regions derived from P-ACT-LB data are indicated by the dark [light] shaded contours.
• Figure 4: The variation of $V_{\rm I}$ in Eq. (\ref{['vhi']}) (left panel) and $V_{\rm I,\sigma}$ (right panel) as functions of $\sigma$ for smFHI-I with $p=2$, shSUGRA $\alpha=0$ and $\beta=-3$ resulting to $n_{\rm s}=0.967$ (solid line) or NSUGRA $\alpha=1/15$ and $\beta=-1$ resulting to $n_{\rm s}=0.972$ (dashed line). The values of $\sigma_\star$ and $\sigma_{\rm f}$ are also depicted.