  An exact analytic calculation is presented for the spectrum of relic
gravitational waves in the scenario of accelerating Universe
$\Omega_{\Lambda}+\Omega_m = 1$. The spectrum formula contains explicitly the
parameters of acceleration, inflation, reheating, and the (tensor/scalar)
ratio, so that it can be employed for a variety of cosmological models. We find
that the spectrum depends on the behavior of the present accelerating
expansion. The amplitude of gravitational waves for the model
$\Omega_{\Lambda}=0.65$ is about $\sim 50 %$ greater than that of the model
$\Omega_{\Lambda}=0.7$, an effect accessible to the designed sensitivities of
LIGO and LISA. The spectrum sensitively depends on the inflationary models with
$a(\tau) \propto |\tau|^{1+\beta}$, and a larger $\beta$ yields a flatter
spectrum, producing more power. The current LIGO results rule out the
inflationary models of $\beta \geq -1.8$. The LIGO with its design sensitivity
and the LISA will also be able to test the model of $\beta=-1.9$. We also
examine the constraints on the spectral energy density of relic gravitational
waves. Both the LIGO bound and the nucleosynthesis bound point out that the
model $\beta=-1.8$ is ruled out, but the model $\beta=-2.0$ is still alive. The
exact analytic results also confirm the approximate spectrum and the numerical
one in our previous work.
