Constraints on Neutrino Secret Interactions from Multi-messenger Neutrinos Scattering on C$\nu$B

We present new constraints on neutrino secret interactions ($\nu$SI) by studying high-energy neutrinos from well-known astrophysical sources, such as SN1987A, the blazars TXS $0506+056$ and PKS $0735+178$, the active galaxy NGC 1068, and the KM3-230213A neutrino event. We expand existing limits by probing a previously unconstrained region of the mediator mass parameter space. Our study focuses on Dirac neutrinos interacting with a massive spin-one boson as they propagate through the Cosmic Neutrino Background, while also examining Majorana and Dirac neutrinos scattering via a scalar mediator. We consider both ultra-relativistic and non-relativistic regimes, establishing bounds on the $\nu$SI coupling constant across the wide $\nu$SI mediator mass range. Our results, obtained using analytical methods, demonstrate significant constraints on the $\nu$SI vector coupling in the low mediator mass region, compared to the scalar coupling scenario.