Isocurvature and adiabatic fluctuations of the axion in chaotic inflation models and large scale structure

In chaotic inflation models, quantum fluctuations from axion fields lead to overproduction of domain walls and overly large isocurvature fluctuations, which is inconsistent with observations of cosmic microwave back-ground anisotropies. These problems are solved by assuming a very flat potential for the Peccei-Quinn scalar field. As the simplest possibility, we consider a model where the Peccei-Quinn scalar is an inflation itself, and show that the isocurvature fluctuations can be comparable with the adiabatic ones. We investigate the cosmological implications of the case when both adiabatic and isocurvature fluctuations exist, and find that the amplitude of the matter spectrum becomes smaller than that for the pure adiabatic case. This leads to a relatively high bias parameter ($b\simeq 2$) which is favored by the current observations.