We propose that the state of the universe does {\it not} spontaneously
violate CPT. Instead, the universe before the Big Bang is the CPT reflection of
the universe after the bang. Phrased another way, the universe before the bang
and the universe after the bang may be re-interpreted as a
universe/anti-universe pair, created from nothing. CPT selects a unique vacuum
state for the QFT on such a spacetime, which leads to a new perspective on the
cosmological baryon asymmetry, and a new explanation for the observed dark
matter abundance. In particular, if we assume that the matter fields in the
universe are described by the standard model of particle physics (including
right-handed neutrinos), we predict that one of the heavy neutrinos is stable,
and that its density automatically matches the observed dark matter density if
its mass is $4.8\times10^{8}~{\rm GeV}$. Among other predictions, we have: (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. We mention connections to the strong CP problem and the
arrow of time.