Axion cosmology in the presence of nontrivial Nambu-Goldstone modes

Axion cosmology is reexamined taking into account the effect of kinetic pseudo-Nambu-Goldstone modes. When Peccei-Quinn (PQ) symmetry is broken by a chiral U(1) singlet, we find that the effect of the kinetic Nambu-Goldstone mode makes the axion dark matter untenable. When PQ symmetry is extended and is broken by two singlets, we find that axion cosmology works, but there are several differences from the axion cosmology studied in the literature. The differences are (1) an ordinary type of dark matter scaling of 1/cosmic scale factor3 arising from a modulus field and not from the usual angular field, (2) the mass of the dark matter quantum in the ultralight range (10-32-10-14) eV, (3) the emergence of dark energy with a present density of order (a few meV)4, consistent with observations, (4) the presence of a long-range spin-dependent force, and (5) slow-roll inflation after PQ symmetry breaking when conformal coupling to gravity is introduced.