$f(R)$引力中的空间曲率
Spatial Curvature in $f(R)$ Gravity
摘要：
在这项工作中，我们考虑四个$f(R)$重力模型-胡-Sawicki，Starobinsky，指数和Tsujikawa模型-并使用一系列的宇宙学数据，连同马尔可夫链蒙特卡罗抽样技术，以约束相关的模型参数。我们的主要目的是比较我们得到的结果时，$Ω_{k,0}$被视为一个自由的参数与他们的同行在空间平坦的情况下。在前一种情况下，我们得到的$Ω_{k,0}$的边界与平坦几何相容。然而，哈勃常数$H_0$越大，曲率越大。事实上，在我们的分析中包括一个高斯似然构造从本地测量的$H_0$，我们发现，结果有利于一个开放的宇宙略高于$1σ$。这也许在统计学上并不重要，但它强调了哈勃张力对通常关于空间曲率的假设的重要影响。我们注意到，哈勃参数与其$Λ$ CDM等效值的后期偏差在所有四个模型中是相当的，特别是在非平坦的情况下。当$Ω_{k,0}=0$时，Hu-Sawicki模型允许$Ω_{\text{cdm},0}h^2$的较小平均值，这增加了在高于1的红移处的所述偏差。我们还研究了规模的变化的影响，通过评估在两个不同的波数$k_\dagger$的增长率。总体而言，任何变化都可以忽略不计，尽管较小的$k_\dagger$确实会导致偏差参数$b$的平均值略大。
英文摘要：
In this work, we consider four $f(R)$ gravity models -- the Hu-Sawicki, Starobinsky, Exponential and Tsujikawa models -- and use a range of cosmological data, together with Markov Chain Monte Carlo sampling techniques, to constrain the associated model parameters. Our main aim is to compare the results we get when $Ω_{k,0}$ is treated as a free parameter with their counterparts in a spatially flat scenario. The bounds we obtain for $Ω_{k,0}$ in the former case are compatible with a flat geometry. It appears, however, that a higher value of the Hubble constant $H_0$ allows for more curvature. Indeed, upon including in our analysis a Gaussian likelihood constructed from the local measurement of $H_0$, we find that the results favor an open universe at a little over $1σ$. This is perhaps not statistically significant, but it underlines the important implications of the Hubble tension for the assumptions commonly made about spatial curvature. We note that the late-time deviation of the Hubble parameter from its $Λ$CDM equivalent is comparable across all four models, especially in the non-flat case. When $Ω_{k,0}=0$, the Hu-Sawicki model admits a smaller mean value for $Ω_{\text{cdm},0}h^2$, which increases the said deviation at redshifts higher than unity. We also study the effect of a change in scale by evaluating the growth rate at two different wavenumbers $k_\dagger$. Any changes are, on the whole, negligible, although a smaller $k_\dagger$ does result in a slightly larger average value for the deviation parameter $b$.
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