Localized Steps toward ACT-Favored Inflation

Abstract

Recent ACT measurements favor a scalar spectral index n_s larger than the Planck value, posing a challenge to many single-field slow-roll inflation models. We show that a smooth, localized step in the inflaton potential can shift the predicted values of n_s and r by displacing the field value at which the CMB pivot scale exits the horizon. This mechanism can move monomial and, in particular, plateau-like attractor models toward the ACT-favored region, whereas the induced shift remains insufficient in natural inflation.

Figures (3)

• Figure 1: Starobinsky potentials with a localized step feature for $\gamma=0$, $\gamma>0$, and $\gamma<0$, normalized at their respective $\phi_\ast$. Colored dashed lines and dots indicate the corresponding $\phi_\ast$ and $\phi_{\rm e}$ at fixed $N_\ast=60$.
• Figure 2: Evolution of $\phi$ with the number of $e$-folds $N$ for the monomial potential with $p=1/10$, shown for $\gamma<0$, $\gamma=0$, and $\gamma>0$.
• Figure 3: Theoretical predictions in the $(n_s,r)$ plane for representative single-field inflation models, with and without a localized step in the potential. The red shaded region shows the constraint from the Planck-LB-BK18 combination AtacamaCosmologyTelescope:2025nti, where LB denotes the inclusion of CMB lensing ACT:2023kunCarron:2022eyg and BAO data DESI:2024uvrDESI:2024mwx, and BK18 refers to the BICEP/Keck 2018 likelihood BICEP:2021xfz. The blue shaded region shows the corresponding constraint from the Planck-ACT-LB-BK18 combination AtacamaCosmologyTelescope:2025nti, which further includes ACT data AtacamaCosmologyTelescope:2025blo, with lensing and BAO information taken from ACT+Planck ACT:2023kunCarron:2022eyg and DESI DESI:2024uvrDESI:2024mwx, respectively. Solid curves without markers show the predictions of the unmodified models at $N_{*}=60$: monomial inflation with $p=1/10$ (red), the $\alpha$-attractor T-model with $n=1$ (brown), the $\alpha$-attractor E-model with $n=1$ (black), and natural inflation (blue). Colored curves and filled markers show the corresponding predictions with a step modulation. For the monomial potential, $p=1/10$ and $M=1/100M_{\mathrm{pl}}$ are fixed; the two parameter sets are $(\gamma,\Delta\phi/M_{\mathrm{pl}})=(0.025,0.143)$ with $\phi_{c}/M_{\mathrm{pl}}=\{4.5,4.0,3.5,3.0\}$ (red circles), and $(\gamma,\Delta\phi/M_{\mathrm{pl}})=(-0.008,0.143)$ with $\phi_{c}/M_{\mathrm{pl}}=\{3.66,3.6,3.5,3.0\}$ (red squares). For the T-model and E-model, $n=1$, $\gamma=0.1$, and $\Delta\phi=0.286M_{\mathrm{pl}}$ are fixed; the representative choices are $\alpha=2$ with $\phi_{c}/M_{\mathrm{pl}}=\{6.2,5.9,5.6,4.8\}$ (brown circles) and $\alpha=1$ with $\phi_{c}/M_{\mathrm{pl}}=\{4.5,4.0,3.5,3.0\}$ (black circles). For natural inflation, $f=6\,M_{\mathrm{pl}}$, $\gamma=-0.5$, and $\Delta\phi=1.0M_{\mathrm{pl}}$, with $\phi_{c}/M_{\mathrm{pl}}=\{14.0,12.0,11.3,9.0\}$ (blue circles). All benchmark choices satisfy the separation condition in Eq. \ref{['eq:CMB_far_step']} and the controlled-deviation conditions in Eq. \ref{['eq:step_sr_cond']}.