Title: Growth of perturbations in nonlocal gravity with non-$Λ$CDM background Show Chinese title

Title: 非局部引力中扰动的增长：非$Λ$冷暗物质背景

Abstract: We re-analyze the nonlocal gravity model of Deser and Woodard which was proposed to account for the current phase of cosmic acceleration. We show that the growth of perturbations predicted by this nonlocal gravity model when its background evolution is fixed by some particular non-$\Lambda$CDM models can be substantially lower than when its background is fixed by $\Lambda$CDM. This can be seen when we consider the background expansion by a dark energy model with a slightly less negative equation of state with respect to cosmological constant. Our results hints towards a fact that the choice of the background expansion can play a crucial role how this nonlocal gravity model can fit the growth history data. While the growth data might show better consistency to GR models (among the background models we studied so far), it seems the nonlocal gravity model studied in this work is able to show comparable consistency to the growth data as well. Showing this consistency can be considered as a significant result since this model can stand as a distinguishable alternative to the standard model of cosmology. Show Chinese abstract

Abstract: 我们重新分析了Deser和Woodard提出的非局域引力模型，该模型旨在解释当前宇宙加速膨胀的阶段。 我们表明，当通过某些特定的非$\Lambda$冷暗物质（CDM）模型固定此非局域引力模型的背景演化时，所预测的扰动增长可以显著低于当其背景由$\Lambda$冷暗物质（CDM）模型固定时的情况。 这一点可以通过考虑一个暗能量模型来观察，该模型具有比宇宙常数稍微不那么负的物态方程。 我们的结果暗示了一个事实，即背景膨胀的选择可能在多大程度上影响这个非局域引力模型如何拟合增长历史数据。 虽然增长数据可能显示出与广义相对论（GR）模型更好的一致性（在我们研究过的背景模型中），但似乎本研究中的非局域引力模型也能够表现出与增长数据相当的一致性。 展示这种一致性可以被视为一个重要结果，因为该模型可以作为宇宙学标准模型的一个可区分的替代方案。