Our universe is filled with stochastic gravitational waves (GWs) with a large range of frequencies, which may have various astrophysical/cosmological origins in the early universe. In this talk I will briefly review the properties of stochastic GWs induced by the scalar perturbation, as well as its connection to the phenomenology of primordial black holes (PBHs). Recently, NANOGrav reported the discovery of a common-spectrum process of the time residuals in their 12.5-yr data set of pulsar timing array, which might be the first detection of stochastic GWs. Based on the recent developments on the spectral shape of such waves, I will show that this signal could be connected to the planet-mass PBH candidates observed by OGLE recently.
