Sterile Neutrino Dark Matter from Generalized $CPT$-Symmetric Early-Universe Cosmologies

We generalize gravitational particle production in a radiation-dominated $CPT$-symmetric universe to non-standard, but also $CPT$-symmetric early universe cosmologies. We calculate the mass of a right-handed "sterile" neutrino needed for it to be the cosmological dark matter. Since generically sterile neutrinos mix with the Standard Model active neutrinos, we use state-of-the-art tools to compute the expected spectrum of gamma rays and high-energy active neutrinos from ultra-heavy sterile neutrino dark matter decay. We demonstrate that the sterile neutrinos are never in thermal equilibrium in the early universe. We show that very high-energy Cherenkov telescopes might detect a signal for sterile neutrino lifetimes up to around 10$^{27}$ s, while a signal in high-energy neutrino telescopes such as IceCube could be detectable for lifetimes up to 10$^{30}$ s, offering a better chance of detection across a vast landscape of possible masses.