AI 中文总结
研究类胡-萨维奇$f(R)$模型与ΛCDM偏差，采用遗传算法结合相关代码，先依理论条件测试$f(R)$函数，再用可行候选者重建背景宇宙学并对比数据，发现偏差有限，有效暗能量状态方程演化微弱。
AI 中文摘要
我们研究了可行的类胡-萨维奇$f(R)$模型是否能产生与ΛCDM的偏差，以便与当前背景宇宙学数据进行对比。采用基于遗传算法（GA）的机器学习方法，在胡-萨维奇模型类周围重建解析微扰。开发了将GATO GA代码与CANDI宇宙学代码连接的管道。由GA生成的每个$f(R)$函数首先根据理论可行性条件进行测试，包括稳定性、标准物质主导时期的恢复、广义相对论极限和变色龙屏蔽机制。可行候选者再传入CANDI重建相应的背景宇宙学，并与DESI DR2 BAO测量和Pantheon+ Ia型超新星目录进行对比。我们发现偏差在后期最大，在更高红移处迅速被抑制。计算$Om(z)$诊断量，其显示与恒定的ΛCDM行为只有非常小的偏离。与重建$f(R)$函数相关的有效暗能量状态方程演化也很微弱。总体而言，结果表明在胡-萨维奇模型类周围的微扰范围内，当前背景数据仅允许与ΛCDM有有限偏差。
英文摘要
We investigate whether viable Hu-Sawicki-like $f(R)$ models can produce deviations from $Λ\mathrm{CDM}$ that can be tested against current background cosmological data. We adopt a machine-learning approach based on Genetic Algorithms (GA) to reconstruct analytical perturbations around the Hu-Sawicki class of models. We develop a pipeline that interfaces the \texttt{GATO} GA code with the \texttt{CANDI} cosmology code. Each $f(R)$ function generated by the GA is first tested against theoretical viability conditions, including stability, the recovery of a standard matter-dominated epoch, the General Relativity limit, and chameleon screening mechanism. Viable candidates are then passed to \texttt{CANDI} to reconstruct the corresponding background cosmology and are tested against DESI DR2 BAO measurements and the Pantheon+ Type Ia supernova catalogue. %\newline The deviations we find are largest at late times, where the lower curvature makes modified-gravity effects more relevant, and are rapidly suppressed at higher redshift, in agreement with the imposed matching to the matter-dominated era. To further quantify deviations from the standard cosmological model, we compute the $Om(z)$ diagnostic. It shows only a very small departure from the constant $Λ\mathrm{CDM}$ behaviour. The effective dark energy equation of state associated with the reconstructed $f(R)$ function also evolves only weakly, showing a mild transition from an effective quintessence-like nature to an effective phantom-like regime. Overall, our results indicate that, within perturbations around the Hu-Sawicki class of models, current background data allow only limited deviations from $Λ\mathrm{CDM}$.
CommentsPrepared for submission to PRD. 15 pages and 5 figures
