AI 中文总结
研究广义纳什引力理论中的宇宙演化，通过相空间分析幂律族及约束正则观测分支，利用多种观测数据，发现其膨胀历史接近\(\Lambda\)CDM且二次修正受严格约束，给出\(\beta\)的背景水平约束。
AI 中文摘要
我们研究了涉及二次里奇不变量\(\chi = R_{\mu\nu}R^{\mu\nu}\)的广义纳什引力理论中的宇宙演化。分析分为两个互补分支。首先，在平坦FLRW背景下，将幂律族\(f(R,\chi)=R^{\alpha}+\beta\chi\)作为简化自治系统研究，因变量在爱因斯坦 - 希尔伯特极限\(\alpha = 1\)处奇异，相空间分析限于\(\alpha\neq1\)，以\(\alpha = 2\)为代表性二次基准，该基准有类辐射边界构型等，但无完整正则辐射 - 物质 - 德西特序列。其次，约束正则观测分支\(f_{\rm obs}(R,\chi)=R - 2\Lambda+\beta\chi\)，\(\beta\to0\)时精确化为平坦\(\Lambda\)CDM。利用超新星Ia、重子声学振荡和普朗克2018压缩宇宙微波背景距离先验，发现其膨胀历史非常接近\(\Lambda\)CDM，二次修正受严格约束。所得\(\beta\)的限制应解释为该简化处方内的背景水平约束，而非全高阶导数理论的微扰水平可行性测试。
英文摘要
We investigate cosmic evolution in generalized Nash's theory of gravity involving the quadratic Ricci invariant $χ=R_{μν}R^{μν}$. The analysis is divided into two complementary branches. First, we study the power-law family $f(R,χ)=R^α+βχ$ as a reduced autonomous system in a flat FLRW background. Because the adopted variables become singular at the Einstein--Hilbert limit $α=1$, the phase-space analysis is restricted to $α\neq1$, with $α=2$ used as a representative quadratic benchmark. This benchmark contains radiation-like boundary configurations, restricted scaling saddles, and de Sitter-like accelerating endpoints (a stable node away from $α=2$ and non-hyperbolic at the benchmark itself), but not a complete regular radiation-to-matter-to-de Sitter sequence. Second, we constrain the regular observational branch $f_{\rm obs}(R,χ)=R-2Λ+βχ$, which reduces exactly to flat $Λ$CDM when $β\to0$. The Hubble rate is obtained from the reduced $Λ$CDM-connected background branch, integrated over $0\le z\le10$ and matched at higher redshift to a standard radiation+matter+$Λ$ background. Using SNe~Ia, BAO, and Planck~2018 compressed CMB distance priors, we find an expansion history very close to $Λ$CDM, with the quadratic correction tightly constrained around the nested standard-model limit. The resulting bound on $β$ should be interpreted as a background-level constraint within this reduced prescription, not as a perturbation-level viability test of the full higher-derivative theory.
Comments23 pages, 10 figures
