Title: New constraints on $f(R)$ gravity from clusters of galaxies Show Chinese title

Title: 来自星系团的$f(R)$引力的新约束

Abstract: The abundance of massive galaxy clusters is a powerful probe of departures from General Relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and "designer", derived from a fully self-consistent analysis of current samples of X-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds $\log_{10}|f_{R0}| < 4.79$ and $\log_{10}B_0 < 3.75$ at the 95.4 per cent confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high quality cluster growth data for the most massive clusters known out to redshifts $z \sim 0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data. Show Chinese abstract

Abstract: 大质量星系团的丰富度是探测宇宙尺度上偏离广义相对论（GR）的重要探针。 尽管目前恒星和星系测试已施加了严格的限制，但在更大的尺度上，如$f(R)$的替代引力理论仍可以作为有效理论。 在这里，我们展示了从当前X射线选择的星系团样本的完全自洽分析中得出的两个流行的$f(R)$模型——Hu-Sawicki 和“设计者”模型的约束，并考虑了宇宙学和天体物理参数之间的所有协方差。 利用星系团数量计数，结合来自宇宙微波背景（CMB）和由大尺度结构产生的CMB透镜势的最新数据，以及对背景膨胀历史和平均物质密度的其他宇宙学约束，我们分别得到了 Hu-Sawicki（带有$n=1$）和“设计者”模型在95.4%置信水平上的上限$\log_{10}|f_{R0}| < 4.79$和$\log_{10}B_0 < 3.75$。 我们结果的稳健性来自于对最巨大星系团在红移$z \sim 0.5$范围内的高质量星系团增长数据，对系统不确定性的严格控制，包括来自弱引力透镜数据的准确且精确的质量校准，以及在我们数据的质量范围内使用晕质量函数的完整形状。