Two-parameter continuous deformation of Starobinsky inflation as a bridge between Planck and ACT DESI data with $N_{\star }\in (50,60)$

Abstract

We present a family of plateau-type inflationary potentials, eq.~\eqref{Vgeneral}, and analyze a two-parameter $\alpha \beta$-Starobinsky specialization that interpolates continuously between a \emph{maximal} plateau ($V\to V_0$) and a \emph{submaximal} plateau ($V\to V_{\infty }<V_0$), where $V_0$ is the overall scale of the potential. In the $\beta \to 0$ limit our framework reproduces the $\alpha$-Starobinsky predictions $n_s\simeq 1-2/N_{\star }$ and $r\simeq 12\alpha /N_{\star }^2$. For $\beta >0$ with $x_{\star }\gg 1/\beta$ the slow-roll scaling laws change to $n_s\simeq 1-\frac{4}{3N_{\star }},r\simeq \mathcal{C}(\alpha ,\beta )N_{\star }^{-4/3},$ with an explicit coefficient $\mathcal{C}(\alpha ,\beta )$ set by the plateau truncation. This deformation lifts $n_s$ at fixed $N_{\star }$ while further suppressing $r$, reconciling the Planck~2018 constraint $n_s=0.9649\pm 0.0042$ (68\% CL) and BICEP/Keck18 data $r_{0.05}<0.036$ (95\% CL), with the higher central values $n_s\sim 0.97$--$0.98$ preferred by ACT+DESI~DR2 (BAO), within the theoretically motivated interval $N_{\star }\in (50,60)$ and without exotic reheating. We provide an exact identity for $V/V^{\prime }$ enabling analytic control of $N_{\star }$, a practical crossover criterion $\beta x_{\star }\ll 1$ vs.\ $\gg 1$, and a transparent mapping between $(\alpha ,\beta )$ and the observables $(n_s,r,N_{\star })$. These yield sharp, testable signatures, particularly the softened $N_{\star }$-scaling of $r$, that distinguish a maximal from a submaximal plateau with upcoming CMB and LSS data.

arXiv comment13 pages, 4 figures, 1 table