The simple assumption of an instantaneous reionization of the Universe may bias estimates of cosmological parameters. In this paper a model-independent principal component method for the reionization history is applied to give constraints on the cosmological parameters from recent Planck 2015 data. We find that the Universe is not completely reionized at redshifts $z\ge 8.5$ at 95% C.L. Both the reionization optical depth and matter fluctuation amplitude are higher than but consistent with those obtained in the standard instantaneous reionization scheme. The high estimated value of the matter fluctuation amplitude strengthens the tension between Planck cosmic microwave background observations and some astrophysical data, such as cluster counts and weak lensing. The tension can be significantly relieved if the neutrino masses are allowed to vary. Thanks to a high scalar spectral index, the low-scale spontaneously broken supersymmetry inflationary model can fit the data well, which is marginally disfavored at 95% C.L. in the Planck analysis.

• Received 9 September 2015

DOI:https://doi.org/10.1103/PhysRevD.92.123521