Relic gravitational waves and their detection

As strong evidence for inflation, relic gravitational waves (RGW) have been extensively studied. Although they have not been detected yet, some constraints have been achieved by observations. Future experiments for RGW detection are mainly of two kinds: CMB experiments and laser interferometers. In this paper, we study these current constraints and the detective abilities of future experiments. We calculate the strength of RGW Omega(g)(k) using two methods: the analytic method and the numerical method, by solving the inflationary flow equations. By the first method, we obtain a bound Omega(g)< 3.89x10(-16) at nu=0.1 Hz, where we have used the current constraints on the scalar spectral index and the tensor-scalar ratio; furthermore, we have taken into account the redshift-suppression effect, the accelerating expansion effect, and the neutrino damping effect on RGW. But the analytic expression of Omega(g)(k) depends on specific inflationary models and does not apply well for the waves with very high frequencies. The numerical method is more precise for the waves with high frequencies. It gives a bound Omega(g)< 8.62x10(-14), which is independent of the inflationary parameters, and applies to any single-field slow-roll inflationary model. After considering the current constraints on the inflationary parameters, this bound becomes Omega(g)< 2x10(-17). These two methods give consistent conclusions: the current constraints on RGW from LIGO, big bang nucleosynthesis, and pulsar timing are too loose to give any constraint for the single-field inflationary models, and the constraints from WMAP are relatively tighter. Future laser interferometers are more effective for detecting RGW with the smaller tensor-scalar ratio, but the CMB experiments are more effective for detecting the waves with the larger ratio. These detection methods are complementary to each other for the detection of RGW.