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Several authors have pointed out that the scalar-mediated interaction ofneutrinos in a neutriophilic two-Higgs-doublet model (nu2HDM) can be as strongas electromagnetic interaction [1-3]. We show that the coupling constants ofneutrino-scalar interaction are actually restricted to be y_i < 1.5 x 10^{-3}by supernova neutrino observation, and further constrained to be y_i < 2.3 x10^{-4} by precision measurements of acoustic peaks of the cosmic microwavebackground. Based on the energy-loss argument for supernova cores, we derive aslightly more restrictive bound y_i < 3.5 x 10^{-5}. Therefore, the nu2HDM haslost its spirit of explaining tiny Dirac neutrino masses while keeping neutrinoYukawa couplings of order one.

Comment on astrophysical consequences of a neutrinophilic 2HDM