tabulate_3D_variances

randomfield.lensing.tabulate_3D_variances(ell, DA, growth, power)

Tabulate 3D matter-power contributions to shear power variances.

This function is defined as:

\[V(\ell, D_A) = \frac{\pi}{\ell} G(D)^2 \Delta^2_\delta(k=\ell/D_A(D), z=0)\]

where \(D\) is the comoving distance corresponding to the comoving transverse distance \(D_A\) and \(\ell\) is a 2D wavenumber.

Use calculate_shear_power() to calculate the lensing shear power associated with the returned 3D matter-power contributions.

Parameters:

ell : numpy.ndarray

1D array of 2D wavenumbers where shear power variances should be tabulated. Values must be positive and increasing, but do not need to be equally spaced.

DA : numpy.ndarray

1D array of comoving transverse distances \(D_A(z)\) where shear power variances should be tabulated. Values must be positive and increasing, but do not need to be equally spaced. Values can be in either Mpc/h or Mpc, but must be consistent with the power spectrum normalization.

growth : numpy.ndarray

1D array of growth function values \(G(z)\) corresponding to each input \(DA(z)\) value. Must have the same number of elements as DA. Can be calculated using randomfield.cosmotools.get_growth_function().

power : structured numpy.ndarray

Power spectrum to use, which meets the criteria tested by randomfield.powertools.validate_power(). Can be calculated using randomfield.cosmotools.calculate_power() if the optional classy package is installed. Values of k and P(k) can either be in Mpc/h or Mpc units, but must be consistent with the values of DA.

Returns:

numpy.ndarray

Two dimensional array with shape (nell, nDA) where nell = len(ell) and nDA = len(DA). The value out[i,j] gives the contribution to the shear variance \(\Delta^2_{EE}\) at 2D wavenumber ell[i] from lensing by mass inhomogeneities at comoving transverse distance DA[j]. The output is dimensionless.