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, so that the state of the universe does {\it not} spontaneously violate CPT. The universe before the bang and the universe after the bang may be viewed as a universe/anti-universe pair, created from nothing. The early universe is radiation dominated and inflationary energy is not required. We show how CPT selects a preferred vacuum state for quantum fields on such a cosmological spacetime. This, in turn, leads to a new view of the cosmological matter/anti-matter asymmetry, and a novel and economical explanation of the dark matter abundance. If we assume that the matter fields in the universe are described by the standard model of particle physics (including right-handed neutrinos), it is natural for one of the heavy neutrinos to be stable, and we show that in order to match the observed dark matter density, its mass must be $4.8\times10^{8}~{\rm GeV}$. We also obtain further predictions, including: (i) that the three light neutrinos are majorana; (ii) that the lightest of these is exactly massless; and (iii) that there are no primordial, long-wavelength gravitational waves.