Two-parameter continuous deformation of Starobinsky inflation as a bridge between Planck and ACT DESI data with N⋆∈(50,60)
Abstract
We present a family of plateau-type inflationary potentials, eq.~\eqref{Vgeneral}, and analyze a two-parameter αβ-Starobinsky specialization that interpolates continuously between a \emph{maximal} plateau (V → V0) and a \emph{submaximal} plateau (V → V∞<V0), where V0 is the overall scale of the potential. In the β → 0 limit our framework reproduces the α-Starobinsky predictions ns≃ 1−2/N⋆ and r≃ 12α/N⋆2. For β>0 with x⋆≫ 1/β the slow-roll scaling laws change to ns≃ 1−4/3N⋆, r≃𝒞(α,β) N⋆−4/3, with an explicit coefficient 𝒞(α,β) set by the plateau truncation. This deformation lifts ns at fixed N⋆ while further suppressing r, reconciling the Planck~2018 constraint ns=0.9649±0.0042 (68\% CL) and BICEP/Keck18 data r0.05<0.036 (95\% CL), with the higher central values ns∼0.97--$0.98$ preferred by ACT+DESI~DR2 (BAO), within the theoretically motivated interval N⋆∈(50,60) and without exotic reheating. We provide an exact identity for V/V' enabling analytic control of N⋆, a practical crossover criterion β x⋆≪1 vs.\ ≫1, and a transparent mapping between (α,β) and the observables (ns,r,N⋆). These yield sharp, testable signatures, particularly the softened N⋆-scaling of r, that distinguish a maximal from a submaximal plateau with upcoming CMB and LSS data.
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BibTeX
@misc{german2026twoparameter,
title = {{Two-parameter continuous deformation of Starobinsky inflation as a bridge between Planck and ACT DESI data with $N_\star\in(50,60)$}},
author = {G. German},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10991},
eprint = {2609.10991},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10991},
}
RIS
TY - UNPB
TI - Two-parameter continuous deformation of Starobinsky inflation as a bridge between Planck and ACT DESI data with N_⋆∈(50,60)
AU - G. German
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.10991
UR - https://arxiv.org/abs/2609.10991
AB - We present a family of plateau-type inflationary potentials, eq.~\eqref{Vgeneral}, and analyze a two-parameter αβ-Starobinsky specialization that interpolates continuously between a \emph{maximal} plateau (V → V_0) and a \emph{submaximal} plateau (V → V_∞<V_0), where V_0 is the overall scale of the potential. In the β → 0 limit our framework reproduces the α-Starobinsky predictions n_s≃ 1−2/N_⋆ and r≃ 12α/N_⋆^2. For β>0 with x_⋆≫ 1/β the slow-roll scaling laws change to n_s≃ 1−4/3N_⋆, r≃𝒞(α,β) N_⋆^−4/3, with an explicit coefficient 𝒞(α,β) set by the plateau truncation. This deformation lifts n_s at fixed N_⋆ while further suppressing r, reconciling the Planck~2018 constraint n_s=0.9649±0.0042 (68\% CL) and BICEP/Keck18 data r_0.05<0.036 (95\% CL), with the higher central values n_s∼0.97--$0.98$ preferred by ACT+DESI~DR2 (BAO), within the theoretically motivated interval N_⋆∈(50,60) and without exotic reheating. We provide an exact identity for V/V' enabling analytic control of N_⋆, a practical crossover criterion β x_⋆≪1 vs.\ ≫1, and a transparent mapping between (α,β) and the observables (n_s,r,N_⋆). These yield sharp, testable signatures, particularly the softened N_⋆-scaling of r, that distinguish a maximal from a submaximal plateau with upcoming CMB and LSS data.
ER -