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High energy neutrinos and anti-neutrinos ($\gtrsim$ 100 GeV) can injectenergetic electromagnetic particles into the baryon-photon plasma in the highredshift universe through electroweak showers from electroweak bremsstrahlung,inelastic scattering with the background electrons and nucleons, and bypair-production of standard model particles on background neutrinos andanti-neutrinos. In this paper, we evolve the particle cascades of high energynon-thermal neutrinos injections, using dark matter decay as a specificexample, including relevant collision processes of these neutrinos with thebackground particles and taking into account the expansion of the universe. Westudy the effect of these non-thermal neutrino injections on the CMB spectralshape and abundance of light elements produced in the big bang nucleosynthesis.We show that CMB spectral distortions and abundance of light elements canconstrain neutrino energy density at the recombination, parameterized ascontribution to $N_{\rm{eff}}$, from high energy neutrino injection. Theseconstraints are stronger by several orders of magnitudes compared to the CMBanisotropy constraints. We also show that CMB spectral distortions can probeneutrino injections to significantly higher redshifts ($z>2\times 10^6$) ascompared to pure electromagnetic energy injection.

journal of cosmology and astroparticle physics

Constraints on $N_{\rm{eff}}$ of high energy non-thermal neutrino  injections upto $z\sim 10^8$ from CMB spectral distortions and abundance of  light elements