Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant

Pseudoscalars appear frequently in particle spectra. They can be light if they appear as pseudo-Goldstone bosons from some spontaneously broken global symmetries with the decay constant f. Since any global symmetry is broken at least by quantum gravitational effects, all pseudoscalars are massive. The mass scale of a pseudoscalar is determined by the spontaneous symmetry breaking scale f of the corresponding global symmetry and the explicit breaking terms in the effective potential. The explicit breaking terms can arise from anomaly terms with some non-Abelian gauge groups among which the best-known example is the potential of the QCD axion. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms in the potential in which case the leading term suppressed by f determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a quintessential axion. In the other extreme that the breaking scales are large, still the pseudo-Goldstone boson mass scales are in general smaller than the decay constants. In such a case, still the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model. We review these ideas in the bosonic collective motion framework.