Adiabatic and isocurvature fluctuations of Affleck–Dine field in D-term inflation model

We reconsider fluctuations of Affleck–Dine (AD) field in a D-term inflation model. Contrary to the previous analysis, we find that the spectrum of the adiabatic fluctuations is almost scale invariant even if the AD field has a large initial value. Furthermore, we study the isocurvature fluctuations of the AD field and estimate the ratio of the isocurvature to adiabatic power spectrum. The dynamics of the inflaton and AD fields sets the upper bound for the value of the AD field, leading to a lower limit for isocurvature perturbation. It is shown that the recent cosmic microwave background data give a constraint on the D-term inflation and the AD field.