AI 中文总结
研究利用巨脉泽观测数据，通过马尔可夫链蒙特卡罗方法约束HuSawicki、Starobinsky、ArcTanh三种f(R)引力模型及ΛCDM模型参数，发现各模型哈勃常数与其他数据一致，f(R)模型与ΛCDM在统计上难区分，物质密度受弱约束。
AI 中文摘要
在这项工作中，我们研究了三种广泛使用的f(R)引力模型，即HuSawicki、Starobinsky和ArcTanh模型，以及标准宇宙学模型（ΛCDM）。为此，我们采用了巨脉泽宇宙学项目的巨脉泽角直径距离和速度测量数据，这些数据提供了哈勃常数的纯几何测定。我们使用马尔可夫链蒙特卡罗方法来约束参数。结果表明，所有四个模型得到的哈勃常数H₀值与其他晚期观测数据（如Ia型超新星）得到的值一致。所有研究模型对H₀的约束都很严格，边缘化估计值接近73 km s⁻¹ Mpc⁻¹。三个f(R)引力模型的偏差参数b的边缘化估计值接近零。因此，这个晚期数据集预测f(R)模型模仿ΛCDM。然而，所有模型的物质密度Ωm仍然受到弱约束，其边缘化估计值接近0.5。此外，使用赤池信息准则和贝叶斯信息准则等信息标准对四个模型（f(R)模型和ΛCDM）进行比较表明，在当前不确定性范围内，该数据集发现f(R)模型与ΛCDM在统计上无法区分。这与每个f(R)模型的b的偏好值接近零这一事实是一致的。
英文摘要
In this work, we study three widely used models of f(R) gravity, namely HuSawicki, Starobinsky and ArcTanh along with the standard cosmology model ($Λ$CDM). For this, we employ the megamaser angular diameter distance and velocity measurements from the Megamaser Cosmology Project, which provide a purely geometric determination of the Hubble constant. We constrain the parameters using the Markov Chain Monte Carlo method. Our results show that values of the Hubble Constant, $H_{0}$, obtained for all four models are in concordance with its value obtained from other late-time observational data such as SNe Ia. The constraints on $H_{0}$ in all the models under study are restrictive and the marginalized estimates lie close to 73 $\mathrm {km s^{-1} Mpc^{-1}}$. The marginalized estimates of the deviation parameter, b, for the three f(R) gravity models lie close to zero. This late-time dataset, thus predicts that f(R) models mimic $Λ$CDM. However, the matter density, $Ω_m$, remains weakly constrained for all the models with its marginalized estimate close to 0.5. Further, comparison of the four models (f(R) models and $Λ$CDM) using information criteria such as Akaike Information Criterion and Bayesian Information Criterion shows that within current uncertainties, the dataset finds f(R) models statistically indistinguishable from $Λ$CDM. This is consistent with the fact that the favoured value of b for each of the f(R) models lies close to zero.
Comments18 pages, 6 tables, 8 figures
Journal ref2026 Res. Astron. Astrophys. 26 125011
