The general potential of power-law inflation is as $V (ϕ) \propto ϕ^{n}$ $V (ϕ) \propto ϕ^{n}$ with scalar field $ϕ$ $ϕ$ . The behavior of inflation is often known as power-law expansion like $S (η) \propto η^{1 + β}$ $S (η) \propto η^{1 + β}$ with $1 + β < 0$ $1 + β < 0$ . 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 $β$ $β$ and $n$ $n$ . Also, the obtained constraints indicate that special types of the potential of inflation, prototype, and KKLTI models, which are originated from string theory, may be good candidates for potential of inflation. Also these results may emphasize the evidence of stochastic GWs that originated from inflation based on 12:5-year pulsar timing data set of North American Nanohertz Observatory for GWs.

Keywords:

PACS: 13.15.+g, 98.80.Es, 98.70.Vc

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