content_image/344643.jpg content_image/344646.jpg
<img src='content_image/344643.jpg'>

fractional energy density can be estimated by following Eq. (403), given by [783, 784] $^{86}$: 

<img src='content_image/344646.jpg'>

The scalar field is dominating the energy density of the universe at the time of fragmentation. For physically motivating parameters, we have chosen; m ∼ 100 GeV, φ ( t ) ∼ 10 16 GeV, and H ( t ) ∼ 1 GeV, therefore, for a reasonable value of K ∼ 0 . 1, we obtain, Ω$_{GW}$ ∼ 10 − $^{6}$. Including the cosmological expansion, the current abundance of gravity waves will be: Ω$_{GW}$ h 2 ∼ 10 − $^{11}$, where h ∼ 0 . 7 is the Hubble constant, with a peak frequency ranging from mHz –10 Hz. Note that Ω$_{GW}$ depends on the value of K , for K = 0 there are no excitations of gravity waves, see Fig. (18). 

