Relic gravitational waves and their detection

As the strong evidence for inflation, the relic gravitational waves (RGW) have been extensively studied. Although, it has not been detected, yet some constraints have been achieved by the observations. Future experiments for the RGW detection are mainly two kinds: the CMB experiments and the laser interferometers. In this paper, we study these current constraints and the detective abilities of future experiments. We calculate the strength of RGW Ωg(k) in two methods: the analytic method and the numerical method by solving the inflationary flow equations. By the first method we obtain a bound Ωg < 3.89 × 10−16 at ν = 0.1Hz, where we have used the current constraints on the scalar spectral index, the tensor-scalar ratio, furthermore, we have taken into account of the redshift-suppression effect, the accelerating expansion effect, the neutrino damping effect on the RGW. But the analytic expression of Ωg(k) depends on the specific inflationary models and not well applies for the waves with very high frequencies. The numerical method is more precise for the waves with high frequencies and applies to any single-field inflationary model. It gives a bound Ωg < 8.62×10−14, 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 Ωg < 2 × 10−17. These two methods give the consistent conclusions: the current constraints on the 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. The future laser interferometers are more effective on detecting the 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. PACS numbers: 98.80.-k, 98.80.Es, 04.30.-w, 04.62.+v e-mail: [email protected]