Relic Gravitational Waves and the Detection

As the “smoking-gun” evidence for inflation, the relic gravitational waves (RGW) have been studied by a lot of authors. Although, it hasn’t been detected until now, some constraints have been achieved by the observations. Future experiments for the RGW detection are mainly two kinds: the CMB (cosmic microwave background radiation) experiments and the laser interferometers. In this paper, we study how tight of these current constraints and the detective abilities of future experiments by calculating the strength of RGW Ωg(k) in two methods: the analytic method and the numerical method by solving the inflationary flow equations. The former method has a simple and clear physical meaning, and gives a bound Ωg < 3.89× 10−16, after considering the current constraints on ns (scalar spectral index) and r (tensor-scalar ratio) and the reashift-suppression effect, the accelerating expansion effect, the neutrino damping effect of the RGW, where Ωg is the strength of RGW at ν = 0.1Hz (the sensitive frequency of laser interferometers). But the value of Ωg(k) depends on an undetermined parameter r, which is dependent on the specific inflationary models, and the expression of primordial spectrum isn’t good enough for the waves with very high frequency. The latter method is more precise for the high frequency waves and applies to any singlefield inflationary model. It gives a bound Ωg < 8.62 × 10−14, which is independent on the inflationary parameters, and applies to any single-field slow-roll inflationary model. After considering the current constraints on ns, r and α (the running of scalar spectral index), this bound becomes Ωg < 2 × 10−17. These two methods give the consistent conclusions: The current constraints on the RGW from LIGO, BBN (big bang nucleosynthesis) and pulsar timing are too loose to give any constraint for the single-field inflationary models, and the constraint from WMAP are relatively tighter. The future laser interferometers are more effective for detecting the RGW with smaller r, but the CMB experiments are more effective for detecting the waves with larger r. They are complementary to each other for the RGW detection. PACS numbers: 98.80.-k, 98.80.Es, 04.30.-w, 04.62.+v e-mail: [email protected]