Are latest detected events of gravitational waves in favor of some models of inflation based on string theory?

The general potential of power-law inflation is as $V(\varphi )\propto {\varphi }^n$ with scalar field $\varphi$. The behavior of inflation is often known as power-law expansion like $S(\eta )\propto {\eta }^{1+\beta }$ with $1+\beta <0$. In this paper, the theoretical spectra of relic gravitational waves are compared with the measured strain sensitivity of Advanced LIGO and VIRGO, corresponding to the latest detected events of gravitational waves. The results show tight constraints on $\beta$ and $n$. Also, the obtained constraints indicate that special types of the potential of inflation, prototype, and KKLTI models, which are originated from string theory, are more suitable than other models. Our analysis shows that there exist some more chances for the detection of relic gravitational waves.