content_image/356656.jpg content_image/356657.jpg content_image/356658.jpg content_image/356659.jpg content_image/356661.jpg content_image/356660.jpg
## V. THE STOCHASTIC BACKGROUND OF GRAVITATIONAL WAVES FROM KINKS 

We have found Eqs. (45),(46) and (47) as the total energy radiated per unit time in a horizon from kinks on an infinite string. Now we are in a position to calculate the density parameter of GWs defined by 

<img src='content_image/356656.jpg'>

where ρ$_{c}$ denotes the critical energy density of the present Universe. Noting that the energy density of GWs decreases as a − 4 and the frequency redshifts as a − $^{1}$, we get 

where a ( t ) is the scale factor and a$_{0}$ represents its present value. Using Eqs. (45),(46) and (47), we get the spectrum as 

<img src='content_image/356657.jpg'>

<img src='content_image/356658.jpg'>

where 

<img src='content_image/356659.jpg'>

<img src='content_image/356661.jpg'>

<img src='content_image/356660.jpg'>

where t$_{0}$ and T$_{0}$ denote the present age and temperature of the Universe, T$_{r}$ is the reheating temperature and H ∗ is the Hubble parameter at the end of inflation. 6 This formula has 

