Abstract
In this paper, we improve the calculation of the relic gravitational waves (RGW) in two aspects: First, we investigate the transfer function after considering the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependent relations on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW at a very wide frequency range, where the observed constraints on
n
s
(the scalar spectral index) and
P
S
(
k
0
)
(the amplitude of primordial scalar spectrum) and the Hamilton-Jacobi equation are used. This method is applied to two kinds of inflationary models, which all satisfy the current constraints on
n
s
,
α
(the running of
n
s
) and
r
(the tensor-scalar ratio). We plot them in the
r−
Ω
g
diagram, where
Ω
g
is the strength of RGW, and study their detection by the CMB experiments and laser interferometers.