约束$f(R)$引力与演化暗能量：基于大尺度结构和相空间轨迹
Constraining $f(R)$ gravity and evolving dark energy via large-scale structure and phase-space trajectories
- University of Cape Town（开普敦大学）
- Universidad de Salamanca（萨拉曼卡大学）
- Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学-西班牙国家科学研究委员会理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文联合BAO、超新星、CMB和增长数据约束Hu-Sawicki与Starobinsky$f(R)$模型参数，并构建相空间零检验以探测对$\Lambda$CDM的偏离，发现模型在AIC下受支持但BIC下证据减弱。
AI中文摘要：
我们提出一项联合观测分析，将可行的$f(R)$修正引力理论（具体为Hu \\& Sawicki和Starobinsky模型）与背景及大尺度结构（LSS）数据相对照。利用蒙特卡洛马尔可夫链（MCMC）采样，数据集包括重子声学振荡（BAO）、Ia型超新星（SNeIa）、宇宙微波背景（CMB）距离先验以及线性增长测量（$f\sigma_8$、$f$、$\sigma_8$），我们对控制偏离广义相对论的模型参数施加了严格约束。对于完整数据集组合，我们得到Hu \\& Sawicki模型的$\log_{10} b_\mathrm{HS} = -6.325_{-1.138}^{+1.216}$和Starobinsky模型的$b_\mathrm{S} = (0.8\pm61.0)\times10^{-4}$。基于赤池信息准则的模型比较表明，这些$f(R)$扩展在统计上优于平坦$\Lambda\text{CDM}$（$|\Delta\text{AIC}| \ge 3.99$）对于组合数据。然而，当考虑贝叶斯信息准则时，支持证据显著减少。此外，我们在$z$多个红移处构建了$(\mu, \gamma)$和$(\mu, \Sigma)$平面中的二维相空间图，建立了一种新颖的诊断零检验，使我们能够利用LSS观测量探测对$\Lambda\text{CDM}$的偏离，对应两个平面中的固定点$(1,1)$。如果未来的弱透镜和星系巡天提供$\mu-1<0$且$\gamma-1>1$或$\Sigma-1 < 0$的数据点，则上述模型可能被直接排除。
英文摘要：
We present a joint observational analysis confronting viable $f(R)$ modified gravity theories, specifically the Hu \& Sawicki and Starobinsky models, with background and large-scale structure (LSS) data. Utilizing Monte-Carlo Markov chain (MCMC) sampling across datasets including baryon acoustic oscillations (BAO), type Ia supernovae (SNeIa), cosmic microwave background (CMB) distance priors, and linear growth measurements ($fσ_8$, $f$, $σ_8$), we place tight constraints on the model parameters governing deviations from General Relativity. For the full dataset combination, we obtain $\log_{10} b_\mathrm{HS} = -6.325_{-1.138}^{+1.216}$ for the Hu \& Sawicki model and $b_\mathrm{S} = (0.8\pm61.0)\times10^{-4}$ for the Starobinsky model. Model comparison based on the Akaike Information Criterion indicates that these $f(R)$ extensions are statistically favored over flat $Λ\text{CDM}$ ($|Δ\text{AIC}| \ge 3.99$) for the combined data. However, when considering the Bayesian Information Criterion, the evidence for support is significantly reduced. Furthermore, we construct two-dimensional phase-space diagrams in the $(μ, γ)$ and $(μ, Σ)$ planes across several redshifts, establishing a novel diagnostic null-test allowing us to probe for deviations from $Λ\text{CDM}$, corresponding to the fixed point $(1,1)$ in both planes, using LSS observables. Should future weak-lensing and galaxy surveys provide data points with $μ-1<0$ and $γ-1>1$ or $Σ-1 < 0 $, then the aforementioned models could be directly ruled out.
