Dynamics of Q-Balls in an expanding universe
  We analyse the evolution of light Q-balls in a cosmological background, and find a number of interesting features. For Q-balls formed with a size comparable to the Hubble radius, we demonstrate that there is no charge radiation, and that the Q-ball maintains a constant physical radius. Large expansion rates cause charge migration to the surface of the Q-ball, corresponding to a non-homogeneous internal rotation frequency. We argue that this is an important phenomenon as it leads to a large surface charge and possible fragmentation of the Q-ball. We also explore the deviation of the Q-ball profile function from the static case. By introducing a parameter $\epsilon$, which is the ratio of the Hubble parameter to the frequency of oscillation of the Q-ball field, and using solutions to an analytically approximated equation for the profile function, we determine the dependence of the new features on the expansion rate. This allows us to gain an understanding of when they should be considered and when they can be neglected, thereby placing restrictions on the existence of homogeneous Q-balls in expanding backgrounds. 
Eran Palti, P.M. Saffin, E.J. Copeland