变色龙$f(R)$引力中的层次聚类
Hierarchical clustering in chameleon $f(R)$ gravity
摘要：
我们使用一套高分辨率的最先进的N体暗物质模拟的变色龙$f(R)$引力研究高阶体积平均相关函数$\bar{ξ_n}$连同分层$n$ -阶相关振幅$S_n=\barξ_n/\barξ_2^{n-1}$和密度分布函数（PDF）。我们表明，在重力的非线性修改的层次标度的减少累积量被保存。然而，这是由$\bar{ξ_n}$和$S_n$的值以及它们相对于广义相对论重力（GR）的尺度依赖性的显著变化来表征的。此外，我们测量到非线性$σ_8$参数的显著增加，达到$14, 5$，并且对于我们的$f(R)$模型的三种口味，超过GR值0.5%。我们进一步注意到，在小尺度$R\simlt 30\hmpc$下，我们所有的模型的$f(R)$重力都显着增加了约化累积量的值。相反，在$f(R)$中，分层振幅$S_n$的值较小，这表明修改后的重力密度分布函数偏离GR情况。此外，我们还发现在高和中等红移$1\leq z \leq4$处，$f(R)$等级关联振幅的相对偏差的红移演化最快。这些偏差的增长在低红移宇宙中显著减慢。我们还计算PDF，并表明，对于低于$\sim 20\hmpc$的尺度，他们显着转移到低密度的$f(R)$重力。最后，我们讨论了我们的理论预测的星系红移巡天测量的层次集群的影响，包括星系偏置和红移空间扭曲的重要问题。
英文摘要：
We use a suite of high resolution state-of-the-art N-body Dark Matter simulations of chameleon $f(R)$ gravity to study the higher order volume averaged correlation functions $\bar{ξ_n}$ together with the hierarchical $n$-th order correlation amplitudes $S_n=\barξ_n/\barξ_2^{n-1}$ and density distribution functions (PDF). We show that under the non-linear modifications of gravity the hierarchical scaling of the reduced cumulants is preserved. This is however characterised by significant changes of both the $\bar{ξ_n}$ and $S_n$'s values and their scale dependence with respect to General Relativity gravity (GR). In addition, we measure a significant increase of the non linear $σ_8$ parameter reaching $14, 5$ and 0.5% in excess of the GR value for the three flavours of our $f(R)$ models. We further note that the values of the reduced cumulants up to order $n=9$ are significantly increased in $f(R)$ gravity for all our models at small scales $R\simlt 30\hmpc$. In contrast the values of the hierarchical amplitudes, $S_n$'s, are smaller in $f(R)$ indicating that the modified gravity density distribution functions are deviating from the GR case. Furthermore we find that the redshift evolution of relative deviations of the $f(R)$ hierarchical correlation amplitudes is fastest at high and moderate redshifts $1\leq z \leq4$. The growth of these deviations significantly slows down in the low redshift universe. We also compute the PDFs and show that for scales below $\sim 20\hmpc$ they are significantly shifted in $f(R)$ gravity towards the low densities. Finally we discuss the implications of our theoretical predictions for measurements of the hierarchical clustering in galaxy redshifts surveys, including the important problems of the galaxy biasing and redshifts space distortions.
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