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The cosmic microwave background (CMB) places strong constraints on models ofdark matter (DM) that deviate from standard cold DM (CDM), and on initialconditions 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 ofultralight axions (ULAs). This represents the first use of CMB lensing to testthe 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 onthe ULA contribution to the DM, improving by up to a factor of two compared tothe case with temperature anisotropies alone. Axion DM also provides alow-energy window onto the high-energy physics of inflation through theinterplay between the vacuum misalignment production of axions and isocurvatureperturbations. We perform the first systematic investigation into the parameterspace of ULA isocurvature, using an accurate isocurvature transfer function atall $m_{a}$ 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 largeinflationary Hubble parameter, $H_I\sim 10^{14}\text{ GeV}$. The window ofco-existence will be fully probed by proposed CMB-S4 observations withincreased 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 twoindependent measurements of $H_I$ in the CMB using the axion DM content andisocurvature, and the tensor contribution to $B$-modes.

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