Thermal gravitational-wave background in the general pre-inflationary scenario

We investigate the primordial gravitational waves (PGWs) in the general scenario where the inflation is preceded by a pre-inflationary stage with the effective equation of state w. Comparing with the results in the usual inflationary models, the power spectrum of PGWs is modified in two aspects: one is the mixture of the perturbation modes caused by he presence of the pre-inflationary period, and the other is the thermal initial state formed at the Planck era of the early Universe. By investigating the observational imprints of these modifications on the B-mode polarization of cosmic microwave background (CMB) radiation, we obtain the constraints on the conformal temperature of the thermal gravitational-wave background T 63.5 for the model with w=1/3, and N>65.7 for that with w=1. By taking into account various noises and the foreground radiations, we forecast the detection possibility of the thermal gravitational-wave background by the future CMBPol mission, and find that if r>0.01, the detection is possible as long as T>1.5× 10−4 Mpc−1. However, the effect of different w is quite small, and it seems impossible to determine its value from the potential observations of CMBPol mission.