We present a new study on the elastic scattering cross section of dark matter ( DM ) and neutrinos using the latest cosmological data from Planck and large-scale structure experiments . We find that the strongest constraints are set by the Lyman- \alpha forest , giving \sigma _ { DM - \nu } \lesssim 10 ^ { -33 } \left ( m _ { DM } / GeV \right ) { cm% ^ { 2 } } if the cross section is constant and a present-day value of \sigma _ { DM - \nu } \lesssim 10 ^ { -45 } \left ( m _ { DM } / GeV \right ) { cm% ^ { 2 } } if it scales as the temperature squared . These are the most robust limits on DM–neutrino interactions to date , demonstrating that one can use the distribution of matter in the Universe to probe dark ( “ invisible ” ) interactions . Additionally , we show that scenarios involving thermal MeV DM and a constant elastic scattering cross section naturally predict ( i ) a cut-off in the matter power spectrum at the Lyman- \alpha scale , ( ii ) N _ { eff } \sim 3.5 \pm 0.4 , ( iii ) H _ { 0 } \sim 71 \pm 3 ~ { } { \mathrm { km } } ~ { } { \mathrm { s } } ^ { -1 } ~ { } { \mathrm { Mpc } } ^ { -1 } and ( iv ) the possible generation of neutrino masses .