Updated constraints on massive neutrino self-interactions from cosmology
  in light of the $H_0$ tension
  We have updated the constraints on flavour universal neutrino
self-interactions mediated by a heavy scalar, in the effective 4-fermion
interaction limit. We use the relaxation time approximation to modify the
collisional neutrino Boltzmann equations, which is known to be very accurate
for this particular scenario. Based on the latest CMB data from the Planck 2018
data release as well as auxiliary data we confirm the presence of a region in
parameter space with relatively strong self-interactions which provides a
better than naively expected fit. However, we also find that the most recent
data, in particular high-$\ell$ polarisation data from the Planck 2018 release,
disfavours this solution even though it cannot yet be excluded. Our analysis
takes into account finite neutrino masses (parameterised in terms of $\sum
m_{\nu}$) and allows for a varying neutrino energy density (parameterised in
terms of $N_{\rm eff}$), and we find that in all cases the neutrino mass bound
inferred from cosmological data is robust against the presence of neutrino
self-interactions. Finally, we also find that the strong neutrino
self-interactions do not lead to a high value of $H_0$ being preferred, i.e.\
this model is not a viable solution to the current $H_0$ discrepancy.
