Axions and the strong CP problem

Current upper bounds on the neutron electric dipole moment constrain the physically observable quantum chromodynamic (QCD) vacuum angle $|overline{ensuremath{theta}}|ensuremath{lesssim}{10}^{ensuremath{-}11}$. Since QCD explains a great deal of experimental data from the $100phantom{rule{0.3em}{0ex}}mathrm{MeV}$ to the TeV scale, it is desirable to explain this smallness of $|overline{ensuremath{theta}}|$ in the QCD framework; this is the strong $CP$ problem. There now exist two plausible solutions to this problem, one of which leads to the existence of a very light axion. The axion decay constant window, ${10}^{9}ensuremath{lesssim}{F}_{a}ensuremath{lesssim}{10}^{12}phantom{rule{0.3em}{0ex}}mathrm{GeV}$ for an $O(1)$ initial misalignment angle ${ensuremath{theta}}_{1}$, has been obtained from astrophysical and cosmological data. For ${F}_{a}ensuremath{gtrsim}{10}^{12}phantom{rule{0.3em}{0ex}}mathrm{GeV}$ with ${ensuremath{theta}}_{1}