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Nonstandard self-interactions can alter the evolution of cosmologicalneutrinos, mainly by damping free streaming, which should leave traces incosmological observables. Although overall effects are opposite to thoseproduced by neutrino mass and a larger $N_{\rm eff}$, they cannot be totallycanceled by these last. We harness cosmological data that includes CosmicMicrowave Background from Plank 2018, BAO measurements, local $H_0$,Ly-$\alpha$ and SNIa, to constrain massive neutrino self-interactions with avery light scalar mediator. We find that the effective coupling constant, atthe 95\% C.L., should be $g_{\rm eff}< 1.94 \times 10^{-7}$ for only Planck2018 data and $1.97\times10^{-7}$ when Planck + BAO are considered. This boundrelaxes to $2.27\times 10^{-7}$ ($2.3\times 10^{-7}$) for $H_0$($H_0$+SNe+Ly-$\alpha$) data. Using the Planck + BAO dataset, the $H_0$ tensionlowers from 4.3$\sigma$ (for $\Lambda$CDM) to 3.2$\sigma$. The AkaikeInformation Criterion penalizes the self-interacting model due to its largerparameter space for Plank or Planck + BAO data, but favors the interactingmodel when we use local $H_0$ measurements. A somewhat larger value for $H_0$is preferred when we include the whole data pool, which comes accompanied witha larger value of $N_{\rm eff}$ and a more constricted bound on $\Sigma m_\nu$.

Massive neutrino self-interactions with a light mediator in cosmology