We consider extensions of the Standard Model in which a spontaneously broken global chiral Peccei-Quinn ( PQ ) symmetry arises as an accidental symmetry of an exact Z _ { N } symmetry .
For N = 9 or 10 , this symmetry can protect the accion – the Nambu-Goldstone boson arising from the spontaneous breaking of the accidental PQ symmetry – against semi-classical gravity effects , thus suppressing gravitational corrections to the effective potential , while it can at the same time provide for the small explicit symmetry breaking term needed to make models with domain wall number N _ { DW } > 1 , such as the popular Dine-Fischler-Srednicki-Zhitnitsky ( DFSZ ) model ( N _ { DW } = 6 ) , cosmologically viable even in the case where spontaneous PQ symmetry breaking occurred after inflation .
We find that N = 10 DFSZ accions with mass m _ { A } \approx 3.5 \textendash 4.2 \mathrm { meV } can account for cold dark matter and simultaneously explain the hints for anomalous cooling of white dwarfs .
The proposed helioscope International Axion Observatory – being sensitive to solar DFSZ accions with mass above a few meV – will decisively test this scenario .