Axion cold dark matter in view of BICEP2 results

The properties of axions that constitute 100% of cold dark matter (CDM) depend on the tensor-to-scalar ratio $r$ at the end of inflation. If $r=0.20^{+0.07}_{-0.05}$ as reported by the BICEP2 collaboration, then "half" of the CDM axion parameter space is ruled out. Namely, the Peccei-Quinn symmetry must be broken after the end of inflation, and axions do not generate non-adiabatic primordial fluctuations. The cosmic axion density is then independent of the tensor-to-scalar ratio $r$, and the axion mass is expected to be in a narrow range that however depends on the cosmological model before primordial nucleosynthesis. In the standard $\Lambda$CDM cosmology, the CDM axion mass range is $m_a = \left(71 \pm 2\right) \mu{\rm eV} \, (\alpha^{\rm dec}+1)^{6/7}$, where $\alpha^{\rm dec}$ is the fractional contribution to the cosmic axion density from decays of axionic strings and walls.