Fate of global symmetries in the Universe: QCD axion, quintessential axion and trans-Planckian inflaton decay-constant

摘要

Pseudoscalars appearing in particle physics are reviewd systematically. Fromthe fundamental point of view at an ultra-violat completed theory, they can belight if they are realized as pseudo-Goldstone bosons of some spontaneouslybroken global symmetries. The spontaneous breaking scale is parametrized by thedecay constant $f$. The global symmetry is defined by the lowest order termsallowed in the effective theory consistent with the gauge symmetry in question.Since any global symmetry is known to be broken at least by quantumgravitational effects, all pseudoscalars should be massive. The mass scale isdetermined by $f$ and the explicit breaking terms $\Delta V$ in the effectivepotential and also anomaly terms $\Delta\Lambda^4_G$ for some non-Abelian gaugegroups $G$. The well-known example by non-Abelian gauge group breaking is thepotential for the "invisible" QCD axion, via the Peccei-Quinn symmetry, whichconstitutes a major part of this review. Even if there is no breaking termsfrom gauge anomalies, there can be explicit breaking terms $\Delta V$ in thepotential in which case the leading term suppressed by $f$ determines thepseudoscalar mass scale. If the breaking term is extremely small and the decayconstant is trans-Planckian, the corresponding pseudoscalar can be a candidatefor a `quintessential axion'. In general, $(\Delta V)^{1/4}$ is considered tobe smaller than $f$, and hence the pseudo-Goldstone boson mass scales areconsidered to be smaller than the decay constants. In such a case, thepotential of the pseudo-Goldstone boson at the grand unification scale issufficiently flat near the top of the potential that it can be a good candidatefor an inflationary model, which is known as `natural inflation'. We review allthese ideas in the bosonic collective motion framework.