Tensor Detection Severely Constrains Axion Dark Matter

The recent detection of B-modes by BICEP2 has non-trivial implications for axion dark matter implied by combining the tensor interpretation with isocurvature constraints from Planck. In this paper the measurement is taken as fact, and its implications considered, though further experimental verification is required. In the simplest inflation models $r=0.2$ implies $H_I=1.1\times 10^{14}\text{ GeV}$. If the axion decay constant $f_a<H_I/2\pi$ constraints on the dark matter (DM) abundance alone rule out the QCD axion as DM for $m_a \lesssim 52\chi^{6/7}\,\mu\text{eV}$ (where $\chi>1$ accounts for theoretical uncertainty). If $f_a>H_I/2\pi$ then vacuum fluctuations of the axion field place conflicting demands on axion DM: isocurvature constraints require a DM abundance which is too small to be reached when the back reaction of fluctuations is included. High $f_a$ QCD axions are thus ruled out. Constraints on axion-like particles, as a function of their mass and DM fraction, are also considered. For heavy axions with $m_a\gtrsim 10^{-22}\text{ eV}$ we find $\Omega_a/\Omega_d\lesssim 10^{-3}$, with stronger constraints on heavier axions. Lighter axions, however, are allowed and (inflationary) model-independent constraints from the CMB temperature power spectrum and large scale structure are stronger than those implied by tensor modes.
Comment: 6 pages, 1 figure. v2: Some discussion and references added. v3 Update on QCD discussion. Version accepted for publication in Physical Review Letters