Tensor Interpretation of BICEP2 Results Severely Constrains Axion Dark Matter

The recent detection of $B$ modes by the BICEP2 experiment has nontrivial implications for axion dark matter implied by combining the tensor interpretation with isocurvature constraints from Planck observations. In this Letter 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 $H_I=1.1\times {10}^{14}\mathrm{GeV}$. 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 $m_a\lesssim 52{\chi }^{6/7}\mu \mathrm{eV}$ (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 backreaction of fluctuations is included. High-$f_a$ 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 $m_a\gtrsim {10}^{-22}\mathrm{eV}$ we find ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_d\lesssim {10}^{-3}$, 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.

Figure 1

Constraints in axion parameter space: regions below curves are allowed. The solid red line shows the result of the present work which constrains axions using the measured value of $r={0.2(}_{-0.05}^{+0.07}(\mathrm{shown}\mathrm{in}\mathrm{thin}\mathrm{lines})$ and the Planck constraint on axion isocurvature, $A_I/A_s<0.04$. The dashed red line approximates the loosening of this constraint due to suppression of the axion isocuvature power when $m_a<H_{\text{eq}}$. We also show the 95% exclusion contours of Ref. [43] from CMB (WMAP1) and $\mathrm{CMB}+\mathrm{Lyman}\text{−}\alpha$ forest power spectra, which are significantly stronger than the tensor or isocurvature constraint for intermediate mass axions, and are independent of the inflationary model.