Starobinsky暴胀的双参数连续形变：作为Planck与ACT DESI数据之间桥梁的$N_\star\in(50,60)$
Two-parameter continuous deformation of Starobinsky inflation as a bridge between Planck and ACT DESI data with $N_\star\in(50,60)$
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中文总结 AI 辅助
本文提出双参数αβ-Starobinsky平台势，连续连接最大与次最大平台，在N⋆∈(50,60)内调和Planck与ACT+DESI数据，压低张标比r并提升谱指数n_s。
中文摘要 AI 辅助
我们提出了一族平台型暴胀势，见公式~\eqref{Vgeneral}，并分析了一个双参数$\alpha\beta$-Starobinsky特例，它在\emph{最大}平台（$V\\!\to\\!V_0$）和\emph{次最大}平台（$V\\!\to\\!V_\infty<V_0$）之间连续插值，其中$V_0$是势能的整体标度。在$\beta\\!\to\\!0$极限下，我们的框架重现了$\alpha$-Starobinsky的预言$n_s\simeq 1-2/N_\star$和$r\simeq 12\alpha/N_\star^2$。对于$\beta>0$且$x_\star\gg 1/\beta$，慢滚标度律变为$n_s\simeq 1-\frac{4}{3N_\star},\\, r\simeq\mathcal{C}(\alpha,\beta)\\,N_\star^{-4/3},$其中显式系数$\mathcal{C}(\alpha,\beta)$由平台截断决定。这种形变在固定$N_\star$时提升$n_s$，同时进一步压低$r$，从而在理论上受激发的区间$N_\star\in(50,60)$内，无需奇异的再加热过程，即可调和Planck 2018约束$n_s=0.9649\pm0.0042$（68%置信水平）和BICEP/Keck18数据$r_{0.05}<0.036$（95%置信水平）与ACT+DESI~DR2（BAO）偏好的更高中心值$n_s\sim0.97$--$0.98$。我们提供了$V/V'$的精确恒等式，使得$N_\star$可解析控制，一个实用的交叉判据$\beta\\,x_\star\ll1$对比$\gg1$，以及$(\alpha,\beta)$与可观测量$(n_s,r,N_\star)$之间的透明映射。这些给出了尖锐且可检验的信号，特别是$r$的软化$N_\star$标度，可用于区分最大平台与次最大平台，配合即将到来的CMB和LSS数据。
英文摘要
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 ($V\!\to\!V_0$) and a \emph{submaximal} plateau ($V\!\to\!V_\infty<V_0$), where $V_0$ is the overall scale of the potential. In the $β\!\to\!0$ limit our framework reproduces the $α$-Starobinsky predictions $n_s\simeq 1-2/N_\star$ and $r\simeq 12α/N_\star^2$. For $β>0$ with $x_\star\gg 1/β$ the slow-roll scaling laws change to $n_s\simeq 1-\frac{4}{3N_\star},\, r\simeq\mathcal{C}(α,β)\,N_\star^{-4/3},$ with an explicit coefficient $\mathcal{C}(α,β)$ set by the plateau truncation. This deformation lifts $n_s$ at fixed $N_\star$ while further suppressing $r$, reconciling the Planck~2018 constraint $n_s=0.9649\pm0.0042$ (68\% CL) and BICEP/Keck18 data $r_{0.05}<0.036$ (95\% CL), with the higher central values $n_s\sim0.97$--$0.98$ 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 $V/V'$ enabling analytic control of $N_\star$, a practical crossover criterion $β\,x_\star\ll1$ vs.\ $\gg1$, and a transparent mapping between $(α,β)$ 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.
发表机构
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学研究所）
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