Measuring the primordial gravitational waves from cosmic microwave background and stochastic gravitational wave background observations

Abstract: We constrain the primordial gravitational waves from cosmic microwave background (CMB) and stochastic gravitational wave background (SGWB) observations. SGWB provides the latest way to explore the early universe and the cosmological evolution which can be reflected by primordial gravitational waves. We not only combine LIGO observations with CMB to measure primordial gravitational waves, but also forecast the potential abilities of the LISA detector and PTA projects. In the $\Lambda$CDM+$r$+$n_t$ model, the standard six parameters change slightly from SGWB observations. While the constraints on tensor-to-scalar ratio and tensor spectral index are improved obviously from SGWB observations. FAST projects have a significant impact on tensor-to-scalar ratio and tensor spectral index, namely $r<0.028$ and $n_t=-0.41^{+0.64}_{-0.96}$ at $95\%$ confidence level.