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 HI = 1.1 × 10 14 GeV. If the axion decay constant fa < HI /2π constraints on the dark matter (DM) abundance alone rule out the QCD axion as DM for ma 52χ 6/7 µeV (where χ > 1 accounts for theoretical uncertainty). If fa > HI /2π 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 fa QCD axions are thus ruled out. Constraints on axionlike particles, as a function of their mass and DM fraction, are also considered. For heavy axions with ma 10 −22 eV we find Ωa/Ω d 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. −0.05 has profound implications for our understanding of the initial conditions of the universe [2], and points to an inflationary origin for the primordial fluctuations [3][4][5]. The inflaton also drives fluctuations in any other fields present in the primordial epoch and so the measurement of r, which fixes the inflationary energy scale, can powerfully constrain diverse physics. In this work we will discuss the implications for axion dark matter (DM) in the case that the tensor modes are generated during single-field slow-roll inflation (from now on we simply refer to this as 'inflation') by zero-point fluctuations of the graviton. In this work we assume that the measured value of r both holds up to closer scrutiny experimentally, and is taken to be of primordial origin. We relax these assumptions in our closing discussion. We stress that our conclusions are one consequence of taking this measurement at face value, but also that they apply to any detection of r.The scalar amplitude of perturbations generated during inflation is given by [7]