We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the k-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the ΛCDM and the Hu-Sawicki f(R) models, and compare our numerical results against the elephant suite of N-body simulations, finding very good agreement up to k = 0.27 Mpc^-1 h at z = 0.5 for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from ΛCDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.

我们开发了一个框架来计算红移空间功率谱 (PS)，其内核超出了 Einstein-de Sitter (EdS)，可应用于各种广义宇宙学。我们以最近在 Chen, Vlah & White (2020) 中用于标准宇宙学的形式主义为基础，并利用密度加权速度矩生成函数的扩展，明确区分 k 模式的大小及其与视线方向依赖性。我们计算了物质的 PS 和偏置示踪剂到 1 环微扰理论 (PT)，并表明膨胀具有正确的红外和紫外行为，没有不需要的发散。我们还添加了有效场论 (EFT) 反术语，这对于解释对 PT 的小规模贡献是必要的，并采用 IR 恢复处方来正确模拟由于 Standard-PT 内的大规模散装流导致的 BAO 拖尾。为了证明我们形式主义的适用性，我们将其应用于 ΛCDM 和 Hu-Sawicki f(R) 模型，并将我们的数值结果与 N 体模拟的大象套件进行比较，发现非常吻合对于 PS 的前三个非消失勒让德多极子，在z = 0.5 时k = 0.27 Mpc ^-1 h 。据我们所知，这项工作中提出的模型是迄今为止修正重力的最准确的理论 EFT-PT，是唯一一个能够解释红移空间中线性局部偏差之外的模型。因此，我们认为我们的 RSD 建模是构建理论模板的有前途的工具，以便使用从下一阶段的宇宙学调查（例如 DESI 和 LSST）获得的真实数据来测试与 ΛCDM 的偏差。