Symmetry-Protected $α$-Attractor Hybrid Inflation in Supergravity and Constraints from ACT DR6 and DESI DR2

TL;DR

This work constructs a symmetry-protected supergravity model of hybrid $α$-attractor inflation with a constant uplift generated by a hidden Stueckelberg $U(1)_D$. By using an exact $N$-mapping and a plateau potential $U( ext φ)=V_0(1-e^{-eta ext φ})^2$ (with $eta= ext{√}{2/(3α)}$), the authors show that the uplift leaves inflaton dynamics intact while providing a tunable post-inflation vacuum. They derive the full background evolution, perturbation spectra at next-to-leading order via the Hubble-flow hierarchy, and demonstrate radiative stability against Coleman–Weinberg corrections; the uplift primarily suppresses the tensor-to-scalar ratio by a factor $f^2=(V_0/(V_0+V_{ ext{up}}))^2$ without altering the scalar tilt $n_s$. The model yields $n_s oughly 1-2/N_*$ and $r oughly 12α/N_*^2 imes f^2$, compatible with Planck, ACT DR6, and DESI DR2 within current bounds and offering clear prospects for detection of tensor modes by LiteBIRD and CMB-S4. This framework provides a minimal, UV-complete, and falsifiable benchmark for embedding $α$-attractor inflation in supergravity with controlled uplift and a sequestered post-inflationary vacuum.

Abstract

We present a symmetry-protected supergravity realization of hybrid $α$-attractor inflation with a constant sequestered uplift. The model achieves an exact analytic embedding of the attractor geometry while maintaining vacuum stability and radiative control. The uplift, generated by a hidden Stückelberg $U(1)_D$ sector, preserves the inflaton dynamics and provides an independent handle on the post-inflationary vacuum energy. The framework yields precise next-to-leading-order predictions for the scalar spectral tilt and tensor amplitude, fully consistent with current ACT DR6, DESI DR2, and Planck data. Radiative and geometric corrections remain exponentially suppressed, ensuring the robustness of the inflationary trajectory. This construction offers a minimal, UV-complete, and testable benchmark for embedding $α$-attractor inflation in supergravity, with tensor modes potentially observable by LiteBIRD and CMB-S4.

Figures (2)

• Figure 1: The hybrid $\alpha$-attractor potential and its corresponding slow-roll parameters for $\alpha = 1.0$, $1/3$, and $0.1$. (Left) The potential $V(\phi) = V_0(1 - e^{-\beta\phi})^2 + V_{\mathrm{up}}$ asymptotically approaches a plateau for large $\phi$, with smaller $\alpha$ producing a flatter shape. The dashed line denotes the uplift term $V_{\mathrm{up}}$, while the markers indicate the field values corresponding to $N_* = 60$ e-folds before the end of inflation. (Right) The slow-roll parameters $\epsilon(\phi)$ (solid) and $|\eta(\phi)|$ (dashed) shown in logarithmic scale demonstrate that inflation persists as long as $\epsilon,|\eta| \ll 1$. Smaller $\alpha$ values sustain a longer slow-roll regime, characteristic of plateau-like inflationary models.
• Figure 2: Predictions of hybrid $\alpha$-attractor inflation with constant uplift. Points indicate $N_*=50$ and $60$ for the benchmarks in Table \ref{['tab:nsr_points']}. Observational contours correspond to the combined Planck–LiteBIRD–BK18–DESI analysis. Decreasing $\alpha$ suppresses $r$ nearly vertically, while smaller $f$ (stronger uplift) produces a mild upward shift. The universal scaling $n_s\simeq1-2/N_*$ is maintained throughout.