Using the Full Power of the Cosmic Microwave Background to Probe Axion Dark Matter

The cosmic microwave background (CMB) places strong constraints on models of dark matter (DM) that deviate from standard cold DM (CDM), and on initial conditions beyond the scalar adiabatic mode. Here, the full \textit{Planck} data set (including temperature, $E$-mode polarisation, and lensing deflection) is used to test the possibility that some fraction of the DM is composed of ultralight axions (ULAs). This represents the first use of CMB lensing to test the ULA model. We find no evidence for a ULA component in the mass range $10^{-33}\leq m_a\leq 10^{-24}\text{ eV}$. We put percent-level constraints on the ULA contribution to the DM, improving by up to a factor of two compared to the case with temperature anisotropies alone. Axion DM also provides a low-energy window onto the high-energy physics of inflation through the interplay between the vacuum misalignment production of axions and isocurvature perturbations. We perform the first systematic investigation into the parameter space of ULA isocurvature, using an accurate isocurvature transfer function at all $m_{a}$ values. We precisely identify a "window of co-existence" for $10^{-25}\text{ eV}\leq m_a\leq10^{-24}\text{ eV}$ where the data allow, simultaneously, a $\sim10\%$ contribution of ULAs to the DM, and $\sim 1\%$ contributions of isocurvature and tensors to the CMB power. ULAs in this window (and \textit{all} lighter ULAs) are shown to be consistent with a large inflationary Hubble parameter, $H_I\sim 10^{14}\text{ GeV}$. The window of co-existence will be fully probed by proposed CMB-S4 observations with increased accuracy in the high-$\ell$ lensing power and low-$\ell$ $E$ and $B$-mode polarisation. If ULAs in the window exist, this could allow for two independent measurements of $H_I$ in the CMB using the axion DM content and isocurvature, and the tensor contribution to $B$-modes.