  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-neutrino} < 10^{-33} (m_DM/GeV)
cm^2 if the cross section is constant and a present-day value of
sigma_{DM-neutrino} < 10^{-45} (m_DM/GeV) 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 ~ 3.5 +/- 0.4, (iii) H_0 ~ 71 +/- 3 km/s/Mpc and (iv) the
possible generation of neutrino masses.
