The search for primordial gravitational waves through the B-mode polarization
pattern in the CMB is one of the major goals of current and future CMB experiments.
Besides foregrounds, a potential hurdle in this search is the anisotropic secondary B-mode
polarization generated by the scattering of CMB photons off free electrons produced during
patchy cosmological reionization. Robust predictions of these secondary anisotropies are
challenging because of uncertainties in the reionization history. In this paper we revise
estimates of the reionization-induced B-mode signal by incorporating recent advances in the
understanding of reionization through observations of the Lyman-α forest. To derive these
B-mode estimates, we use high-dynamic-range radiative transfer simulations of reionization
that are calibrated to the Lyα data. These simulations are also consistent with a variety
of other high-redshift observations. We find that around multipoles ` ≈ 100, reionization
induces B-mode power with `(` + 1)C
BB
`
/2π ≈ 4 × 10−6 μK2
. This secondary signal is thus
at the level of the primordial signal with the tensor-to-scalar ratio r < 10−4
, and can increase
by a factor of ∼ 50 if reionization is sourced by highly clustered sources residing in haloes
with mass of ∼ 1011 M. Our findings suggest that the contribution of patchy reionization to
the search for primordial gravitational waves is unlikely to be a concern for currently planned
CMB experiments