The Lyα forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Lyα forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the `renormalization' of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics.

Lyα 森林提供了绘制高红移大尺度结构的最佳方法之一，包括我们对宇宙正午前距离-红移关系的最严格限制。我们描述了如何将 Lyα 森林中的大规模相关性理解为光学深度场累积量的扩展，其本身可以通过偏差扩展与密度场相关。这提供了物质波动的可观测数据和统计数据之间的直接联系，可以系统地计算。我们讨论了复杂的小尺度物理进入预测的方式、备受讨论的速度偏差的起源和大尺度偏差系数的“重整化”。我们的计算是在微扰理论的范围内，但我们也使用峰值背景分割与早期工作取得联系。使用运动方程的结构，我们向微扰理论中的所有阶证明，大尺度通量功率谱变为线性谱乘以与视线角度的余弦的二次方的平方。与星系不同的是，各向同性和各向异性的碎片都受到小尺度物理学的贡献。