The introduction of Dark Matter-neutrino interactions modifies the Cosmic Microwave Background ( CMB ) angular power spectrum at all scales , thus affecting the reconstruction of the cosmological parameters .
Such interactions can lead to a slight increase of the value of H _ { 0 } and a slight decrease of \sigma _ { 8 } , which can help reduce somewhat the tension between the CMB and lensing or Cepheids datasets .
Here we show that it is impossible to solve both tensions simultaneously .
While the 2015 Planck temperature and low multipole polarisation data combined with the Cepheids datasets prefer large values of the Hubble rate ( up to H _ { 0 } = 72.1 ^ { +1.5 } _ { -1.7 } km / s / Mpc , when N _ { eff } is free to vary ) , the \sigma _ { 8 } parameter remains too large to reduce the \sigma _ { 8 } tension .
Adding high multipole Planck polarization data does not help since this data shows a strong preference for low values of H _ { 0 } , thus worsening current tensions , even though they also prefer smaller value of \sigma _ { 8 } .