Domain Wall Problem of Axion and Isocurvature Fluctuations in Chaotic Inflation Models

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We study the domain wall problem of an axion in chaotic inflation models. We show that the production of domain walls does not occurs if the Peccei-Quinn scalar has a flat potential and its breaking Fₐ is larger than 10¹⁵GeV. We find that too large isocurvature fluctuations are produced for such high Fₐ. In order for those isocurvature fluctuations to be consistent with observations of the large scale structure of the universe, the self-coupling constant g and the breaking scale of the Peccei-Quinn scalar should be g ≃ (1-2.8)× 10⁻¹³ and Fₐ ≃ (0.6-1.5)× 10¹⁵GeV, respectively. In particular the value of self-coupling constant is almost the same as that required for a chaotic inflation, which strongly suggests that the Peccei-Quinn scalar itself is an inflaton.