content_image/348390.jpg content_image/348391.jpg content_image/348392.jpg content_image/348393.jpg content_image/348394.jpg content_image/348395.jpg
frequencies ∼ ω are ones which satisfy 

<img src='content_image/348390.jpg'>

In other words, if the interval of kinks with sharpness ∼ ψ is similar to the period of the GW under consideration, these kinks make dominant contribution to the GW. In the first matter era, using Eq. (15), Eq. (34) simplifies to 5 

<img src='content_image/348391.jpg'>

for ω < ( t ∗ /t ) $^{A$_{m}$}$t − $^{1}$. (Here, we set A ≡ 2 ζ − β . A$_{r}$ ≃ − 0 . 92 , A$_{m}$ ≃ − 0 . 8.) For ω > ( t ∗ /t ) $^{A$_{m}$}$t − $^{1}$, ( ψ dN dψ ) − 1 > ω − 1 is satisfied by an arbitrary value of ψ . In Appendix B it is shown that for ω > ( t ∗ /t ) $^{A$_{m}$}$t − 1 the main contribution to ω dP dω comes from the kinks corresponding to the peak of the distribution, i.e. ψ ∼ ( t ∗ /t ) 2 $^{ζ$_{m}$}$. If we denote the value of sharpness of kinks which make dominant contribution to ω dP dω as ψ$_{max}$ ( ω, t ), it is given by 

where 

In the second matter era, ψ$_{max}$ is estimated as 

<img src='content_image/348392.jpg'>

<img src='content_image/348393.jpg'>

<img src='content_image/348394.jpg'>

<img src='content_image/348395.jpg'>

