标题： 德塞尔-伍德瓦德非局部引力模型的复兴：原始非局部形式与局域化公式的比较 显示英文标题

标题： Revival of the Deser-Woodard nonlocal gravity model: Comparison of the original nonlocal form and a localized formulation

摘要： 我们研究了Deser-Woodard（DW）非定域引力模型中扰动增长出现两种相反结果的起源。 一组之前以原始非定域形式分析了该模型，并表明与广义相对论（GR）相比，DW模型中的结构增长被增强，因此得出该模型被排除的结论。 然而，最近另一组通过将模型局部化后重新分析，发现其局部化版本中的增长甚至比GR中的增长被抑制。 问题是这种差异是源于非定域和局部化公式之间的内在区别，还是由于他们对子视界极限的不同实现。 我们证明，只要初始条件设置相同，非定域和局部公式对于线性扰动给出相同的解。 对子视界极限的不同实现导致某些扰动变量表现出不同的瞬态行为；然而，这不会显著影响子视界尺度上的物质扰动增长。 同时，我们还报告了前一组数值计算代码中的一个错误，并验证了在修复该错误后，非定域版本也给出了被抑制的增长。 最后，我们讨论了两组采用的两个有效引力常数的替代定义以及一些开放问题。 显示英文摘要

摘要： We examine the origin of two opposite results for the growth of perturbations in the Deser-Woodard (DW) nonlocal gravity model. One group previously analyzed the model in its original nonlocal form and showed that the growth of structure in the DW model is enhanced compared to general relativity (GR) and thus concluded that the model was ruled out. Recently, however, another group has reanalyzed it by localizing the model and found that the growth in their localized version is suppressed even compared to the one in GR. The question was whether the discrepancy originates from an intrinsic difference between the nonlocal and localized formulations or is due to their different implementations of the sub-horizon limit. We show that the nonlocal and local formulations give the same solutions for the linear perturbations as long as the initial conditions are set the same. The different implementations of the sub-horizon limit lead to different transient behaviors of some perturbation variables; however, they do not affect the growth of matter perturbations at the sub-horizon scale much. In the meantime, we also report an error in the numerical calculation code of the former group and verify that after fixing the error the nonlocal version also gives the suppressed growth. Finally, we discuss two alternative definitions of the effective gravitational constant taken by the two groups and some open problems.