Lensing emission angle

This module calculates the corrections to the standard lensed CMB power spectra results due to time delay and emission angle, following arXiv:1706.02673. This can be combined with the result from the postborn module to estimate the leading corrections to the standard lensing B modes.

Corrections to T and E are negligible, and not calculated. The result for BB includes approximately contributions from reionization, but this can optionally be turned off.

camb.emission_angle.get_emission_angle_powers(camb_background, PK, chi_source, lmax=3000, acc=1, lsamp=None)[source]

Get the power spectrum of \(\psi_d\), the potential for the emission angle, and its cross with standard lensing. Uses the Limber approximation (and assumes flat universe).

Parameters:

  • camb_background – a CAMB results object, used for calling background functions

  • PK – a matter power spectrum interpolator (from camb.get_matter_power_interpolator)

  • chi_source – comoving radial distance of source in Mpc

  • lmax – maximum L

  • acc – accuracy parameter

  • lsamp – L sampling for the result

Returns:

a InterpolatedUnivariateSpline object containing \(L(L+1) C_L\)

camb.emission_angle.get_emission_delay_BB(params, kmax=100, lmax=3000, non_linear=True, CMB_unit='muK', raw_cl=False, acc=1, lsamp=None, return_terms=False, include_reionization=True)[source]

Get B modes from emission angle and time delay effects. Uses full-sky result from appendix of arXiv:1706.02673

Parameters:

  • params – model.CAMBparams instance with cosmological parameters etc.

  • kmax – maximum k (in \({\rm Mpc}^{-1}\) units)

  • lmax – maximum \(\ell\)

  • non_linear – include non-linear corrections

  • CMB_unit – normalization for the result

  • raw_cl – if true return \(C_\ell\), else \(\ell(\ell+1)C_\ell/2\pi\)

  • acc – accuracy setting, increase to test stability

  • lsamp – array of \(\ell\) values to compute output at. If not set, set to sampling good for interpolation

  • return_terms – return the three sub-terms separately rather than the total

  • include_reionization – approximately include reionization terms by second scattering surface

Returns:

InterpolatedUnivariateSpline for \(C_\ell^{BB}\)

camb.emission_angle.get_source_cmb_cl(params, CMB_unit='muK')[source]

Get the angular power spectrum of emission angle and time delay sources \(\psi_t\), \(\psi_\zeta\), as well as the perpendicular velocity and E polarization. All are returned with 1 and 2 versions, for recombination and reionization respectively. Note that this function destroys any custom sources currently configured.

Parameters:

  • params – model.CAMBparams instance with cosmological parameters etc.

  • CMB_unit – scale results from dimensionless, use ‘muK’ for \(\mu K^2\) units

Returns:

dictionary of power spectra, with \(L(L+1)/2\pi\) factors.