The Big Bang, CPT, and neutrino dark matter

We investigate the idea that the universe before the Big Bang is the CPT reflection of the universe after the bang, both classically and quantum mechanically, so that the universe does not spontaneously violate CPT . We show how CPT symmetry selects a preferred vacuum state for quantum fields on a CPT -invariant cosmological background spacetime. The universe before the bang and the universe after the bang may be viewed as a universe/anti-universe pair, emerging directly into the hot, radiation-dominated era we observe in our past. This, in turn, leads to a remarkably economical explanation of the cosmological dark matter. With no additional fields beyond Einstein gravity and the standard model of particle physics (including right-handed neutrinos), a Z₂ symmetry stabilizes one of the right-handed neutrinos. We calculate its abundance in detail and show that, in order to match the observed dark matter density, its mass must be 4 . 8 × 10⁸ GeV . We obtain several further predictions, including: (i) that the three light neutrinos are majorana; (ii) that one of these is exactly massless; and (iii) that, in the absence of an epoch of cosmic inflation, there should be no primordial, long-wavelength gravitational waves. We also briefly discuss the natural origin of the matter-antimatter asymmetry within this picture and possibilities for explaining the cosmological perturbations.