Retrieving cosmological information from small-scale CMB foregrounds II.
  The kinetic Sunyaev Zel'dovich effect
  Recent results of ground-based telescopes, giving high-quality measurements
of the CMB temperature power spectrum on small scales motivate the need for an
accurate model of foregrounds, which dominate the primary signal at these
multipoles. In a previous work, we have shown that cosmological information
could be retrieved from the power spectrum of the thermal Sunyaev Zel'dovich
(SZ) effect. In this work, we introduce a physically-motivated model of the
Epoch of Reionisation (EoR) in the cosmological analysis of CMB data, coherent
on all scales. In particular, at high multipoles, the power spectrum of the
kinetic SZ (kSZ) effect is inferred from a set of cosmological parameters by a
machine-learning algorithm. First including an asymmetric parameterisation of
the EoR history in the Planck 2018 data analysis, we retrieve a value of the
CMB optical depth consistent with previous results but giving a completely
different history of the high-redshift Universe, in which the first luminous
sources light up as early as $z=15$. Considering the latest small-scale data
from the South Pole Telescope (SPT) and letting the cosmology free to vary, we
find that including the new cosmology-dependent tSZ and kSZ spectra help
tighten the constraints on the amplitudes of these two spectra by breaking the
degeneracy between their amplitudes. We report a $5\sigma$ measurement of the
kSZ signal at $\ell=3000$ ($\mathcal{D}_{3000}^\mathrm{kSZ} = 3.3 \pm
0.7~\mu\mathrm{K}^2$, $1\sigma$), marginalised over cosmology, as well as an
upper limit on the patchy signal
$\mathcal{D}_{3000}^\mathrm{pkSZ}<1.58~\mu\mathrm{K}^2$ (95\% C.L.).
Additionally, we find that the SPT data favours slightly earlier reionisation
scenarios than Planck, leading to $\tau = 0.062 \pm 0.012$ and a reionisation
midpoint $z_{\rm re} = 7.9\pm1.1$ ($1\sigma$), in line with constraints from
high-redshift quasars and galaxies.
