Relic gravitational waves in the frame of slow-roll inflation with a
  power-law potential and the detection
  We obtained the analytic solutions of relic gravitational waves (RGWs) for
the slow-roll inflation with a power-law form potential of the scalar field,
$V=\lambda\phi^n$. Based on a reasonable range of $n$ constrained by cosmic
microwave background (CMB) observations, we give tight constraints of the
tensor-to-scalar ratio $r$ and the inflation expansion index $\beta$ for the
fixed scalar spectral index $n_s$. Even though, the spectrum of RGWs in low
frequencies is hardly depends on any parameters, the high frequency parts will
be affected by several parameters, such as $n_s$, the reheating temperature
$T_{RH}$ and the index $\beta_s$ describing the expansion from the end of
inflation to the reheating process. We analyzed in detail all the factors which
would affect the spectrum of RGWs in high frequencies including the quantum
normalization. We found that the future GW detectors SKA, eLISA, BBO and DECIGO
are promising to catch the signals of RGWs.
  Furthermore, BBO and DECIGO have the potential not only to distinguish the
spectra with different parameters but also to examine the validity of the
quantum normalization.
