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