Title: Probing non-standard gravity with the growth index: a background independent analysis Show Chinese title

Title: 用增长指数探测非标准引力：一种背景独立的分析

Abstract: Measurements of the growth index $\gamma(z)$ provide a clue as to whether Einstein's field equations encompass gravity also on large cosmic scales, those where the expansion of the universe accelerates. We show that the information encoded in this function can be satisfactorily parameterized using a small set of coefficients $\gamma_i$ in such a way that the true scaling of the growth index is recovered to better than $1\%$ in most dark energy and dark gravity models. We find that the likelihood of current data is maximal for $\gamma_0=0.74\pm 0.44$ and $\gamma_1=0.01\pm0.46$, a measurement compatible with the $\Lambda$CDM predictions. Moreover data favor models predicting slightly less growth of structures than the Planck LambdaCDM scenario. The main aim of the paper is to provide a prescription for routinely calculating, in an analytic way, the amplitude of the growth indices $\gamma_i$ in relevant cosmological scenarios, and to show that these parameters naturally define a space where predictions of alternative theories of gravity can be compared against growth data in a manner which is independent from the expansion history of the cosmological background. As the standard $\Omega$-plane provides a tool to identify different expansion histories $H(t)$ and their relation to various cosmological models, the $\gamma$-plane can thus be used to locate different growth rate histories $f(t)$ and their relation to alternatives model of gravity. As a result, we find that the Dvali-Gabadadze-Porrati gravity model is rejected with a $95\%$ confidence level. By simulating future data sets, such as those that a Euclid-like mission will provide, we also show how to tell apart LambdaCDM predictions from those of more extreme possibilities, such as smooth dark energy models, clustering quintessence or parameterized post-Friedmann cosmological models. Show Chinese abstract

Abstract: 通过对增长指数 $\gamma(z)$ 的测量，可以初步判断爱因斯坦场方程是否也涵盖了宇宙大尺度上的引力作用，即那些加速膨胀的宇宙区域。我们证明，通过一组小系数集 $\gamma_i$ 来参数化这一函数时，可以很好地恢复增长指数的真实标度，并且在大多数暗能量和暗引力模型中误差小于 $1\%$。我们发现，当前数据的最大似然值出现在 $\gamma_0=0.74\pm 0.44$ 和 $\gamma_1=0.01\pm0.46$，这一测量结果与 $\Lambda$冷暗物质（CDM）预测一致。此外，数据更倾向于预测结构增长略低于普朗克 LambdaCDM 情景的模型。本文的主要目的是提供一种常规分析方法，用于计算相关宇宙场景下增长指数 $\gamma_i$的幅度，并展示这些参数如何自然地定义一个空间，在这个空间内可以独立于宇宙背景的膨胀历史，比较替代引力理论的预测与增长数据。 由于标准的$\Omega$-平面提供了一种工具，用于识别不同的膨胀历史$H(t)$及其与各种宇宙学模型的关系，因此$\gamma$-平面可以用来定位不同的增长速率历史$f(t)$及其与替代引力模型的关系。 因此，我们发现 Dvali-Gabadadze-Porrati 引力模型被排除的可能性达到了$95\%$的置信水平。 通过模拟未来数据集（例如类似 Euclid 任务所提供的数据集），我们也展示了如何区分 LambdaCDM 预测与其他更极端的可能性，如平滑暗能量模型、聚类动力 Quintessence 或参数化后 Friedmann 宇宙学模型。