NumCosmoXcorLensingEfficiency

Abstract class for computing lensing efficiency.

This class provides infrastructure for computing the lensing efficiency function: \begin{equation} g(z) = \int_z^{z_{\max}} dz’ \left(1 - \frac{\chi(z)}{\chi(z’)}\right) W_{\mathrm{src}}(z’) \end{equation} where $W_{\mathrm{src}}(z’)$ is a source weight function that must be implemented by subclasses. The integration is performed using CVODE (BDF method) to solve the equivalent ODE system: \begin{align} \frac{df}{d(-z)} &= -\frac{g}{E(z)} \ \frac{dg}{d(-z)} &= -\frac{W_{\mathrm{src}}(z)}{d_t(z)} - \Omega_{k0} \frac{f}{E(z)} \end{align} where $f(z) = g(z)$, $E(z) = H(z)/H_0$, $d_t(z)$ is the transverse comoving distance, and the integration is performed backwards from $z_{\max}$ to $z \approx 0$.

Subclasses must implement two virtual methods:

• eval_source(): returns $W_{\mathrm{src}}(z)$
• get_z_range(): returns the source redshift range

Example subclasses:

• Weak lensing: $W_{\mathrm{src}}(z) = \frac{dn}{dz}$ (source galaxy distribution)
• Galaxy magnification bias: $W_{\mathrm{src}}(z) = (5s-2) \frac{dn}{dz}$ (weighted by magnification bias parameter).