关于弱宇宙弯曲的Born近似的有效性
On the validity of the Born approximation for weak cosmic flexions
摘要：
弱透镜计算通常是在玻恩近似的假设下进行的，其中光线路径近似为一条直线。此外，透镜-透镜耦合，其中有几个偏转沿光线往往被忽略。我们研究的影响，下降的玻恩近似，并考虑透镜透镜耦合，弱透镜效应到第二阶（宇宙弯曲），通过在光路中的微扰expansion. We提出了一个图形表示的透镜效应的修正。测量密度场导数的弯曲信号获得与平方重力剪切成比例的校正项;我们还发现，通过放弃玻恩近似，除了四个标准弯曲分量之外，还可以激发透镜畸变的两个自由度（扭曲分量）。我们推导出角功率谱的弯曲和扭曲，有和没有玻恩近似和透镜透镜耦合，并确认玻恩近似是一个很好的近似弱宇宙弯曲，除了在非常小的尺度。
英文摘要：
Weak lensing calculations are often made under the assumption of the Born approximation, where the ray path is approximated as a straight radial line. In addition, lens-lens couplings where there are several deflections along the light ray are often neglected. We examine the effect of dropping the Born approximation and taking lens-lens couplings into account, for weak lensing effects up to second order (cosmic flexion), by making a perturbative expansion in the light path. We present a diagrammatic representation of the resulting corrections to the lensing effects. The flexion signal, which measures the derivative of the density field, acquires correction terms proportional to the squared gravitational shear; we also find that by dropping the Born approximation, two further degrees of freedom of the lensing distortion can be excited (the twist components), in addition to the four standard flexion components. We derive angular power spectra of the flexion and twist, with and without the Born-approximation and lens-lens couplings and confirm that the Born approximation is an excellent approximation for weak cosmic flexions, except at very small scales.
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