Radiative transfer effects during primordial helium recombination
  In this paper we refine the calculation of primordial helium recombination,
accounting for several additional effects that were neglected or treated more
approximately in previous studies. These include consideration of (i)
time-dependent radiative transfer interaction between the 2^1 P_1 - 1^1 S_0 and
2^3 P_1 - 1^1 S_0 resonances; (ii) time-dependent radiative transfer for the
partially overlapping n^1 P_1 - 1^1 S_0, n^1 D_2 - 1^1 S_0 and n^3 P_1 - 1^1
S_0 series with 3 <= n <= 10; (iii) electron scattering within a kernel
approach. We also briefly discuss the effect of electron scattering and HI
quadrupole lines on the recombination of hydrogen. Although the physics of all
the considered processes is interesting and subtle, for the standard cosmology,
with Y_p \sim 0.24, the overall correction to the ionization history during
helium recombination with respect to the previous implementation of CosmoRec
remains smaller than |DeltaNe/Ne| \sim 0.05%. The dominant improvement is
caused by consistent inclusion of resonance scattering for the 2^1 P_1 - 1^1
S_0 resonance. For cosmologies with a large helium fraction, Y_p \sim 0.4, the
difference reaches |D N_e/N_e|\sim 0.22% at z\sim1800, however, the overall
correction to the CMB power spectra is small, exceeding |D C_l/C_l| \sim 0.05 %
only at l>\sim 3000. In comparison to the current version of Recfast the
difference reaches |D C_l/C_l|\sim0.4% at l\sim 3000 for Y_p \sim 0.4, and also
for the standard value Y_p \sim 0.24 we find differences |DC_l/C_l|>\sim 0.1%
at l\sim 2500. The new processes are now included by the cosmological
recombination code CosmoRec and can be activated as needed for most settings
without affecting its runtime significantly.
