$CPT$-Symmetric Universe

We propose that the state of the Universe does not spontaneously violate $CPT$. Instead, the Universe after the big bang is the $CPT$ image of the Universe before it, both classically and quantum mechanically. The pre- and postbang epochs comprise a universe-antiuniverse pair, emerging from nothing directly into a hot, radiation-dominated era. $CPT$ symmetry selects a unique QFT vacuum state on such a spacetime, providing a new interpretation of the cosmological baryon asymmetry, as well as a remarkably economical explanation for the cosmological dark matter. Requiring only the standard three-generation model of particle physics (with right-handed neutrinos), a ${\mathbb{Z}}_2$ symmetry suffices to render one of the right-handed neutrinos stable. We calculate its abundance from first principles: matching the observed dark matter density requires its mass to be $4.8\times {10}^8\mathrm{GeV}$. Several other testable predictions follow: (i) the three light neutrinos are Majorana particles and allow neutrinoless double $\beta$ decay; (ii) the lightest neutrino is massless; and (iii) there are no primordial long-wavelength gravitational waves. We mention connections to the strong $CP$ problem and the arrow of time.