Reviving Motivated Inflationary Potentials with $K$-inflation in the light of ACT

Abstract

Recent ACT data favor a higher scalar spectral index $n_s$, placing models such as $\alpha$-attractor T-models and natural Inflation in tension with current observations. We propose a K-inflation framework with a field-dependent non-canonical kinetic term $G(\phi)$ that reconciles these models with the latest Planck-ACT-LB-BK18 constraints. Our analysis includes a refined calculation of the reheating equation-of-state parameter $w_{\rm re}$, avoids standard power-law approximations, and tests consistency with the Swampland Distance and de Sitter Conjectures. We find that the additional friction from the non-minimal kinetic coupling shifts both models into the favored observational regions. For the $\alpha$-attractor T-model with $n=2$, viable solutions occur for $\beta\sim \mathcal{O}(10)$, with Swampland consistency favoring $\alpha\gtrsim \mathcal{O}(10^{-3})$. This case predicts matter-like reheating and a red-tilted gravitational-wave background that is unlikely to be detected soon. In contrast, natural Inflation with $n=4,5$ is compatible with CMB constraints for $\alpha\lesssim 7,8$ and $\beta\lesssim -1$, respectively, leading to stiff reheating and a blue-tilted gravitational-wave background potentially observable by LISA, Cosmic Explorer, Einstein Telescope, DECIGO, and BBO while satisfying BBN and $\Delta N_{\rm eff}$ bounds. Combining gravitational-wave probes with Swampland criteria may therefore help distinguish possible UV completions of inflation.