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arXiv 1802.03403astro-ph.CO
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宇宙弱透镜的规范不变形式

Gauge-Invariant Formalism of Cosmological Weak Lensing

Jaiyul Yoo, Nastassia Grimm, Ermis Mitsou, Adam Amara, Alexandre Refregier

摘要:

我们提出了宇宙学弱透镜的规范不变形式,解释了由于线性量级的标量、矢量和张量扰动引起的所有相对论效应。虽然光的传播完全由测地线方程描述,但光子波矢量与物理量的关系需要定义它们的框架的规范。通过构造观测者和源位置的局部四分体基,我们阐明了弱透镜观测量(如会聚、剪切和转动)与源静止坐标系中定义的物理尺寸和形状以及观测者静止坐标系中测量的观测角和红移之间的关系。与标准的透镜形式主义相比,额外的相对论效应对所有的透镜观测量都有贡献。我们明确验证规范不变性的透镜观测量,并比较我们的结果与以前的工作。特别是,我们证明,即使在存在的矢量和张量扰动,物理旋转的透镜观测值消失在线性顺序,而四分之一的基础旋转沿光传播相比,FRW坐标。虽然后者经常被用作探测原始引力波,但四分体基底的旋转确实不是一个物理观测。进一步阐明了它与弱透镜下的E-B分解的关系。我们的形式主义提供了一个透明的和全面的宇宙学弱透镜的观点。

英文摘要:

We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source rest-frame and the observed angle and redshift measured in the observer rest-frame. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gauge-invariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the E-B decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.

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