We study the detectability of the gravitational waves (GWs) from the $Q$-ball formation associated with the Affleck-Dine (AD) mechanism, taking into account both the dilution effects due to $Q$-ball domination and to finite temperature. The AD mechanism predicts the formation of nontopological solitons, $Q$-balls, from which GWs are generated. $Q$-balls with large conserved charge $Q$ can produce a large amount of GWs. On the other hand, the decay rate of such $Q$-balls is so small that they may dominate the energy density of the Universe, which implies that GWs are significantly diluted and that their frequencies are redshifted during the $Q$-ball dominated era. Thus, the detectability of the GWs associated with the formation of $Q$-balls is determined by these two competing effects. We find that there is a finite but small parameter region where such GWs may be detected by future detectors such as DECIGO or BBO, only in the case when the thermal logarithmic potential dominates the potential of the AD field. Otherwise GWs from $Q$-balls would not be detectable even by these futuristic detectors: ${\Omega }_{\mathrm{GW}}^0<{10}^{-21}$. Unfortunately, for such parameter region the present baryon asymmetry of the Universe can hardly be explained unless one fine-tunes $A$-terms in the potential. However the detection of such a GW background may give us an information about the early Universe, for example, it may suggest that the flat directions with $B-L=0$ are favored.

• Received 24 December 2009

DOI:https://doi.org/10.1103/PhysRevD.81.083503