Secret-Interaction Opacity of the Cosmic Neutrino Background for PeV Neutrinos

If neutrinos have interactions beyond the weak force — 'secret' interactions with a new mediator — then the relic neutrino background filling the universe becomes a target, and sufficiently strongly interacting PeV neutrinos would be absorbed on their way to Earth. This paper computes the opacity of the cosmic background for representative cross sections. For a cross section of 10^-34 square centimetres on the background today, the mean free path is 5.787e+07 Mpc, vastly larger than the observable universe, and the optical depth to redshift 2 is only 3.305e-04. Reaching an optical depth of unity by redshift 1 requires a cross section near 7.779e-31 square centimetres. A resonance, where the centre-of-mass energy matches a mediator mass, concentrates the effect: for 1 PeV neutrinos striking 0.1 eV relic neutrinos, the resonant mediator mass is 0.0141 GeV. Capping the background density growth at redshift 8, as a bounced history with a maximum temperature would, changes the optical depth to redshift 8 not at all at the computed precision — 0.00231 capped against 0.00231 uncapped — because the opacity accumulates at low redshift where the two histories are identical. The study is computed from stated assumptions, not measured.