Conventional and Unitarity-Conserving Peccei-Quinn Inflation Models and ACT

We compare conventional non-minimally coupled Peccei-Quinn (PQ) inflation with a version of the model in which unitarity conservation is imposed by additional Jordan frame interactions. Assuming instantaneous reheating, the unitarity-conserving model is within 1$\sigma$ agreement with the central value of the scalar spectral index reported by the ACT collaboration, whereas conventional PQ inflation is more than 2$\sigma$ below the ACT central value. In the case where dark matter is composed of axions and PQ symmetry is not restored after inflation, the axion isocurvature constraint of the unitarity-conserving model typically allows a much larger axion decay constant $f_{a}$ than the conventional model, with the conventional model upper bound being comparable only if the PQ scalar self-coupling is extremely small, $\lambda \lesssim 10^{-10}$. For $\lambda = 0.1$, the axion isocurvature upper bounds are $f_{a} \lesssim 1.1 \times 10^{9}$ GeV for conventional PQ inflation and $f_{a} \lesssim 6.4 \times 10^{13}$ GeV for unitarity-conserving PQ inflation, with the latter bound being independent of $\lambda$. We also find a new isocurvature upper bound for conventional PQ inflation which is 650 times smaller than the existing bound. A modest reduction of the reheating temperature of the unitarity-conserving model from its maximum possible value will ensure that the PQ symmetry is not restored after inflation, allowing values of $f_{a}$ up to $6.4 \times 10^{13}$ GeV. Thus only the unitarity-conserving PQ inflation model allows $f_{a}$ to access values greater than the symmetry restoration cosmological upper bound $\sim 10^{12}$ GeV with naturally large values of the PQ scalar self-coupling.