Unifying inflation and dark matter with the Peccei-Quinn field: observable axions and observable tensors

A model of high scale inflation is presented where the radial part of the Peccei-Quinn (PQ) field with a non-minimal coupling to gravity plays the role of the inflaton, and the QCD axion is the dark matter. A quantum fluctuation of $\mathcal{O}(H/2\pi)$ in the axion field will result in a smaller angular fluctuation if the PQ field is sitting at a larger radius during inflation than in the vacuum. This changes the effective axion decay constant, $f_a$, during inflation and dramatically reduces the production of isocurvature modes. This mechanism opens up a new window in parameter space where an axion decay constant in the range $10^{12}\text{ GeV}\lesssim f_a\lesssim 10^{15}\text{ GeV}$ is compatible with observably large $r$. The exact range allowed for $f_a$ depends on the efficiency of reheating. This model also predicts a minimum possible value of $r=10^{-3}$. The new window can be explored by a measurement of $r$ possible with \textsc{Spider} and the proposed CASPEr experiment search for high $f_a$ axions.