Inflation models with Peccei–Quinn symmetry and axion kinetic misalignment

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We propose a consistent framework with the U(1) Peccei–Quinn (PQ) symmetry for obtaining the initial condition for axion kinetic misalignment from inflation. We introduce a PQ complex scalar field and an extra Higgs doublet, which are conformally coupled to gravity, and three right-handed neutrinos for the seesaw mechanism. In the DFSZ type scenarios for the axion, we obtain the PQ anomalies from the Standard Model quarks carrying nonzero PQ charges in some of two Higgs doublet models, solving the strong CP problem by the QCD potential for the axion. Assuming that the PQ symmetry is explicitly violated in the scalar potential by quantum gravity effects, we show that a sufficiently large initial axion velocity can be obtained before the QCD phase transition while avoiding the axion quality problem. As inflation is driven by the radial distance from the origin in the space of scalar fields close to the pole of the kinetic terms in the Einstein frame, we obtain successful inflationary predictions and set the initial axion velocity at the end of inflation. Focusing on the pure PQ inflation with a small running quartic coupling for the PQ field, we discuss the post-inflationary dynamics for the inflaton and the axion. As a result, we show that a sufficiently high reheating temperature can be obtained dominantly from the Higgs-portal couplings to the PQ field, while being consistent with axion kinetic misalignment, the stability for the Higgs fields during inflation and the non-restoration of the PQ symmetry after reheating.