Upside Down Inflation: dark matter and reheating after a CPT- symmetric bang

Boyle, Finn and Turok proposed that the universe before the big bang is the CPT image of the one after it, with no inflation, and that the dark matter is a right-handed neutrino 𝑁1 made by the expansion at the bang. Without inflation its mass is at most 491.6 PeV for every CPT-invariant state [1]. Here we add a period of inflation after the bang on each side. CPT symmetry makes a homogeneous inflaton even in conformal time, so it starts at rest. With enough inflation to make the observed perturbations, the choice of state at the bang drops out under the standard assumption that modes far above the temperature start in their vacuum, and the reheating history sets the mass, as for any purely gravitational Majorana fermion, provided the inflaton’s Yukawa coupling to 𝑁1 is below about 𝑀 /20𝑀𝑃 . We also locate where an analytic spectrum for this transition departs from numerical ones. The inflaton must also survive the hot era before inflation and still reheat. A T-model 𝛼-attractor with 𝛼 = 0.0045 supplies the perturbations at 𝐻inf = 1012 GeV, with 𝑟 = 1.6 × 10−5 and 𝑛𝑠 = 0.9655. Coupled to matter through its bounded field, it is shielded from the plasma before inflation, which moves it by 2.0 × 10−5 𝑀𝑃 . A Yukawa coupling to a heavy fermion reheats it to at most 1.2 × 1013 GeV, which puts the dark matter at 561 PeV or heavier. A trilinear coupling to the Higgs through the same field reaches instant reheating with the plateau intact, but meets tachyonic preheating. We close with a hypothesis, kept apart from the rest: that expansion counts the formation of clocks.