Loop corrections to the power spectrum are frequently computed using approximate non-linear kernels adopted from an Einstein de-Sitter (EdS) cosmology. We present an algorithm that allows us to take the full time- and scale-dependence of the underlying fluid dynamics into account, and apply it to assess the impact of neutrino free-streaming on the 1- and 2-loop matter power spectrum. Neutrino perturbations are described by a hybrid Boltzmann/two-fluid model, that we show to agree with the CLASS Boltzmann solution at the linear level when using an appropriate effective neutrino sound velocity. We then use this scheme at 1- and 2-loop to perform a precision comparison of the matter power spectrum with simplified treatments of massive neutrinos. For a commonly adopted scheme using cold dark matter+baryon perturbations and EdS kernels to compute non-linear corrections, we find deviations above 1% for k > 0.15 h/Mpc at z=0, and sub-percent agreement on weakly non-linear scales at z=0.5. We also demonstrate the impact of the EdS approximation on the 2-loop power spectrum for massless neutrinos.

中文翻译：

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对具有完全时间和尺度相关性的大规模中微子宇宙学的功率谱进行环路校正

功率谱的环路校正经常使用从爱因斯坦去西特 (EdS) 宇宙学中采用的近似非线性内核来计算。我们提出了一种算法，使我们能够将基础流体动力学的全部时间和尺度相关性考虑在内，并将其应用于评估中微子自由流动对 1 环和 2 环物质功率谱的影响。中微子扰动由混合玻尔兹曼/双流体模型描述，当使用适当的有效中微子声速时，我们表明在线性水平上与 CLASS 玻尔兹曼解是一致的。然后，我们在 1 环和 2 环中使用此方案，对物质功率谱与大量中微子的简化处理进行精确比较。对于使用冷暗物质 + 重子扰动和 EdS 内核来计算非线性校正的普遍采用的方案，我们发现 k > 0.15 h/Mpc 在 z=0 时偏差高于 1%，并且在弱非线性上的亚百分比一致性在 z=0.5 处缩放。我们还演示了 EdS 近似对无质量中微子的 2 环功率谱的影响。