Asymptotic Behavior of Saxion–Axion System in Stringy Quintessence Model

The late time behavior of the slow-roll parameter in the stringy quintessence model is studied when axion as well as saxion are allowed to move. Even though the potential is independent of the axion at tree level, the axion can move through its coupling to the saxion and the background geometry. Then the contributions of the axion kinetic energy to the slow-roll parameter and the vacuum energy density are not negligible when the slow-roll approximation does not hold. As the dimension of the field space is doubled, the fixed point at which the time variation of the slow-roll parameter vanishes is not always stable. It is found that the fixed point in the saxion–axion system is at most partially stable, in particular when the volume modulus and the axio-dilaton, the essential ingredients of the string compactification, are taken into account. It seems that as more saxion–axion pairs are considered, achieving the stability of the fixed point becomes difficult.