Can neutrino-assisted early dark energy models ameliorate the $H_0$ tension in a natural way?

The idea of neutrino-assisted early dark energy ($\nu$EDE) was introduced with the aim of reducing some of the fine-tuning required in usual early dark energy (EDE) models. The activation of the EDE field around the recombination epoch can arise as a result of a ``neutrino kick" occurring when neutrinos transition from relativistic to nonrelativistic species. We show that although $\nu$EDE can open up the parameter space especially with respect to the initial field value, unfortunately the kick alone is insufficient to provide cosmologically interesting values of the relevant EDE parameters.