FIG. 16: Lumps of Q-matter are formed during the fragmentation of a condensate with a potential given by Eq. (395). of the condensate. A linear perturbation analysis [509] shows that the fluctuations grow exponentially if the following condition is satisfied: k 2 a 2 ( k 2 a 2 + 2 m 2 3 / $_{2}$K ) < 0 . (398) Clearly, the instability band exists for negative K , as expected from the negative pressure arguments [91]. The instability band, k , is in the range [509] 0 < k 2 a 2 < k 2 max a 2 ≡ 2 m 2 3 / 2 | K | , where a is the expansion factor of the universe. The most amplified mode lies in the mid- dle of the band, and the maximum growth rate of the perturbations is determined by ˙ α ∼ | K | m$_{3}$$_{/}$$_{2}$/ 2 [91]. When δφ/φ$_{0}$ ∼ O (1), the fluctuations become nonlinear. This is the time when the homogeneous condensate breaks down into Q-balls and anti-Q-balls $^{84}$. The gravity waves are generated during preheating, as the excitations involve inhomo- geneous, non-spherical, anisotropic motions of the excited scalar modes. As a result, the stress energy tensor receives anisotropic stress-energy contribution. The generation of grav- ity waves were studied in Refs. [727, 777–786]. Typically, the peak frequency of the gravity waves is such that they correspond to the sub-Hubble wavelengths at the time of production. Gravity waves excitations can be studied numerically by following the transverse-traceless 6. Non-perturbative creations of gravity waves 84 In general K and h are not independent quantities but are related to each other by | K | ∼ C ( h $^{2}$/ 16 π $^{2}$). In this regime the evaporation rate is saturated by: Γ$_{Q}$ = 1 Q dQ dt ≃ 1 | K | 3 / 2 ( m M P ) $^{2}$m [509]. Even though coupling is large, i.e. h ∼ O (0 . 1), the decay rate mimics that of a Planck suppressed interaction of the inflating Q -ball with matter fields. 185