We study the bispectrum in Lagrangian perturbation theory. Extending past results for the power spectrum, we describe a method to efficiently compute the bispectrum in LPT, focusing on the Zeldovich approximation, in which contributions due to linear displacements are captured to all orders in a manifestly infrared (IR) safe way. We then isolate the effects of these linear displacements on oscillatory components of the power spectrum like baryon acoustic oscillations or inflationary primordial features and show that the Eulerian perturbation theory (EPT) prescription wherein their effects are resummed by a Gaussian damping of the oscillations arise as a saddle-point approximation of our calculation. These two methods of IR resummation are in excellent agreement at 1-loop in the bispectrum. At tree level, resummed EPT does less well to capture the nonlinear damping of the oscillations, and the LPT calculation does not require an artificial split of the power spectrum into smooth and oscillatory components, making the latter particularly useful for modeling exotic features. We finish by extending our analysis of IR resummation in LPT to N-point functions of arbitrary order.

中文翻译：

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拉格朗日微扰理论中的双谱


我们研究了拉格朗日微扰理论中的双谱。扩展功率谱的过去结果，我们描述了一种在 LPT 中有效计算双谱的方法，重点是 Zeldovich 近似，其中线性位移的贡献以明显红外 （IR） 安全的方式捕获到所有阶次。然后，我们分离出这些线性位移对功率谱振荡分量（如重子声学振荡或膨胀原始特征）的影响，并表明欧拉微扰理论 （EPT） 公式，其中它们的影响由振荡的高斯阻尼来概括，作为我们计算的马鞍点近似。这两种 IR 求和方法在双光谱中的 1 环处非常一致。在树级别，重新求存的 EPT 不太能很好地捕获振荡的非线性阻尼，并且 LPT 计算不需要人为地将功率谱分成平滑和振荡分量，这使得后者对于模拟奇异特征特别有用。最后，我们将 LPT 中 IR 求和的分析扩展到任意阶的 N 点函数。