D-term Instability in Flat Directions and its Cosmological Implication

Abstract

We study dynamics of flat directions in the minimal supersymmetric standard model taking account of its constituent fields. It is found that there exist new instabilities due to the D-term potential and the nature of these instabilities depends on the eccentricity of the orbit. For a roughly circular orbit, it is similar to narrow-band resonance described by the Mathieu equation. For an elliptic orbit, the instabilities exhibit tachyonic nature. In the narrow-band regime, we show that the existence of the instabilities is crucial to the formation of $Q$-balls. The $Q$-ball formation proceeds through quasi-stable state called ``$I$-ball''. The transition from $I$-balls to $Q$-balls is made efficient by the $D$-term instability and during this process some fraction of the charge of the $Q$-ball is emitted. This discovery may revive the scenario which relates the baryon number and dark matter density of the universe. Furthermore, the tachyonic $D$-term instability causes the drastic decay of the flat direction moving in an orbit with relatively large eccentricity. Thus the evolution of flat directions is completely altered by the appearance of this instability.