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 .