Revisiting isocurvature bounds in models unifying the axion with the inflaton

Axion scenarios in which the spontaneous breaking of the Peccei-Quinn symmetry takes place before or during inflation, and in which axion dark matter arises from the misalignment mechanism, can be constrained by Cosmic Microwave Background isocurvature bounds. Dark matter isocurvature is thought to be suppressed in models with axion-inflaton interactions, for which axion perturbations are assumed to freeze at horizon crossing during inflation. However, this assumption can be an oversimplification due to the interactions themselves. In particular, non-perturbative effects during reheating may lead to a dramatic growth of axion perturbations. We perform lattice calculations in two models in which the Peccei-Quinn field participates in inflation. We find that the growth of axion perturbations is such that the Peccei-Quinn symmetry is restored for an axion decay constant $f_A\lesssim10^{16}$-$10^{17}$ GeV, leading to an over-abundance of dark matter, unless $f_A \lesssim 2 \times 10^{11}$ GeV. For $f_A\gtrsim10^{16}$-$10^{17}$ GeV we still find a large growth of axion perturbations at low momentum, such that a naive extrapolation to CMB scales suggests a violation of the isocurvature bounds