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.
