Domain wall and isocurvature perturbation problems in axion models

Axion models have two serious cosmological problems, domain wall and isocurvature perturbation problems. In order to solve these problems we investigate the Linde's model in which the field value of the Peccei-Quinn (PQ) scalar is large during inflation. In this model the fluctuations of the PQ field grow after inflation through the parametric resonance and stable axionic strings may be produced, which results in the domain wall problem. We study formation of axionic strings using lattice simulations. It is found that in chaotic inflation the axion model is free from both the domain wall and the isocurvature perturbation problems if the initial misalignment angle \theta_a is smaller than O(10^{-2}). Furthermore, axions can also account for the dark matter for the breaking scale v \simeq 10^{12-16} GeV and the Hubble parameter during inflation H_{inf} \lesssim 10^{11-12} GeV in general inflation models.