  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.
