Weak Gravitational Lensing - Cosmic Shear

Cosmic Shear

The gravitational lensing by large-scale structure also produces an observable pattern of alignments in background galaxies, but this distortion is only ~0.1%-1% - much more subtle than cluster or galaxy-galaxy lensing. The thin lens approximation usually used in cluster and galaxy lensing does not always work in this regime, because structures can be elongated along the line of sight. Instead, the distortion can be derived by assuming that the deflection angle is always small (see Gravitational Lensing Formalism). As in the thin lens case, the effect can be written as a mapping from the unlensed angular position to the lensed position . The Jacobian of the transform can be written as an integral over the gravitational potential along the line of sight

\frac{\partial \beta_i}{\partial \theta_j} = \delta_{ij} + \int_0^{r_\infty} dr g(r) \frac{\partial^2 \Phi(\vec{x}(r))}{\partial x^i \partial x^j}

where is the comoving distance, are the transverse distances, and

g(r) = 2 r \int^{r_\infty}_r \left(1-\frac{r^\prime}{r}\right)W(r^\prime)

is the lensing kernel, which defines the efficiency of lensing for a distribution of sources .

As in the thin-lens approximation, the Jacobian can be decomposed into shear and convergence terms.

Read more about this topic:  Weak Gravitational Lensing

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