Dark matter component decaying after recombination: lensing constraints with Planck data

It has been recently suggested~\cite{Berezhiani:2015yta} that emerging tension between cosmological parameter values derived in high-redshift (CMB anisotropy) and low-redshift (cluster counts, Hubble constant) measurements can be reconciled in a model which contains subdominant fraction of dark matter decaying after recombination. We check the model against the CMB Planck data. We find that lensing of the CMB anisotropies by the large-scale structure gives strong extra constraints on this model, limiting the fraction as $F<8\%$ at 2\,$\sigma$ confidence level. However, investigating the combined data set of CMB and conflicting low-$z$ measurements, we obtain that the model with $F\approx2\!-\!5$\% exhibits better fit (by 1.5-3\,$\sigma$ depending on the lensing priors) compared to that of the concordance $\Lambda$CDM cosmological model.