$N_{{\rm eff}}$ constraints on light mediators coupled to neutrinos: the dilution-resistant effect

We investigate the impact of new light particles, carrying significant energy in the early universe after neutrino decoupling, on the cosmological effective relativistic neutrino species, $N_{{\rm eff}}$. If the light particles are produced from decoupled neutrinos, $N_{{\rm eff}}$ is predominantly modified through the dilution-resistant effect. This effect arises because the energy stored in the mass of new particles is less diluted than the photon and neutrino energy as the universe expands. Our study comprehensively explores this effect, deriving $N_{{\rm eff}}$ constraints on the couplings of light mediators with neutrinos, encompassing both scalar and vector mediators. We find that the dilution-resistant effect can increase $N_{{\rm eff}}$ by 0.118 and 0.242 for scalar and vector mediators, respectively. These values can be readily reached by forthcoming CMB experiments. Upon reaching these levels, future $N_{{\rm eff}}$ constraints on the couplings will be improved by many orders of magnitude.