  We explore the constraints on the history of reionization from Planck 2015
Cosmic Microwave Background (CMB) data and we derive the forecasts for future
CMB observations. We consider a class of monotonic histories of reionization as
parametrized by two additional extra parameters with respect to the average
optical depth used in the instantaneous reionization modeling. We investigate
the degeneracies between the history of reionization and selected extensions of
the standard cosmological model. In particular, we consider the degeneracies
with the total mass of the neutrino sector and we discuss the possible
correlation between the dark matter annihilation and the duration of
reionization in the CMB. We use an extension to poly-reion model that was
proposed in Hazra and Smoot, JCAP 1711, 028 (2017). We compare the constraints
from Planck 2015 data with the predicted constraints from possible future CMB
mission as LiteBIRD, and we also use the proposed CORE-like specifications as
an example of what higher resolution can bring in addition. We find that the
degeneracy between the average optical depth and the duration of reionization
will be substantially removed by both concepts. Degeneracies between the
reionization history and either the total neutrino mass and properties of dark
matter annihilation will also be improved by future surveys. We find only
marginal improvement in the constraints on reionization history for the higher
resolution in the case of long duration of reionization.
