Detection relic gravitational waves in thermal case by using Adv.LIGO   data of GW150914
  The thermal spectrum of relic gravitational waves causes the new amplitude that called `modified amplitude'. Our analysis shows that, there exist some chances for detection of the thermal spectrum in addition to the usual spectrum by Adv.LIGO data of GW150914 and detector based on the maser light (Dml). The behavior of the inflation and reheating stages are often known as power law expansion like $ S(\eta)\propto \eta^{1+\beta}$, $S(\eta)\propto \eta^{1+\beta_s}$ respectively. The $\beta$ and $\beta_s$ have an unique effect on the shape of the spectrum. We find some upper bounds on the $\beta$ and $\beta_s$ by comparison the usual and the thermal spectrum with the Adv.LIGO and Dml. As this result modifies our information about the nature of the evolution of inflation and reheating stages. 
Basem Ghayour and Jafar Khodagholizadeh
astro-ph.CO