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

Abstract

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 $F_{a}$ is larger than $\sim 10^{15}$GeV. We find that too large isocurvature fluctuations are produced for such high $F_{a}$. 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 $g \simeq (1-2.8)\times 10^{-13}$ and $F_{a} \simeq (0.6-1.5)\times 10^{15}$GeV, 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.