An ultralight pseudoscalar boson

Using a fundamental discrete symmetry, ZN, we construct a two-axion model with the QCD axion solving the strong-$CP$ problem, and an ultralight axion (ULA) with mULA≈10^-22 eV providing the dominant form of dark matter (DM). The ULA is light enough to be detectable in cosmology from its imprints on structure formation, and may resolve the small-scale problems of cold DM. The necessary relative DM abundances occur without fine-tuning in constructions with decay constants fULA~10¹⁷ GeV, and fQCD~10¹¹ GeV. An example model achieving this has $N=24$, and we construct a range of other possibilities. We compute the ULA couplings to the standard model, and discuss prospects for direct detection. The QCD axion may be detectable in standard experiments through the →E·→B and GG couplings. In the simplest models, however, the ULA has identically zero coupling to both GG of QCD and →E·→B of electromagnetism due to vanishing electromagnetic and color anomalies. The ULA couples to fermions with strength g∝1/fULA. This coupling causes spin precession of nucleons and electrons with respect to the DM wind with period t~ months. Current limits do not exclude the predicted coupling strength, and our model is within reach of the CASPEr-Wind experiment, using nuclear magnetic resonance.