Yang+Zhang

The accelerating expansion of the universe at the present stage is a pro-cess that has great implications on the relic gravitational waves (RGW) and CMB. We present calculations, both analytically exact and numer-ical, for the spectrum of RGW in the scenario of accelerating Universe = 1. The results from both calculations are consistent with each other. The analytic 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. The spectrum is found to depend on the behavior of the present accelerating expansion, and there are new features associated with the acceleration in the result-ing spectrum. In the low frequency range the peak of spectrum is now located at a frequency //, //where is the Hubble frequency, and there appears a new segment of spectrum between  and. In all other intervals of frequencies, the spectral amplitude acquires an extra factor  , due to the current acceleration, otherwise the shape of spectrum is similar to that in the decelerating models. The recent WMAP result of CMB anisotropies is used to normalize the amplitude for RGW. The amplitude of RGW for the model =0//.//65 is about 50% greater than that of the model = 0//.//7, an effect accessible to the designed sensitivities of LIGO and LISA. The spectrum sensitively depends on the in°ationary models with, and a larger  yields a flatter spectrum, producing more power. The current LIGO re-sults rule out the in°ationary models of. The LIGO with its design sensitivity and the LISA will also be able to test the model of = -1.9. We also examine the constraints on the spectral energy den-sity of RGW. Both the LIGO bound and the nucleosynthesis bound point out that the model = //-//1//.//8 is ruled out, but the model  = //-//2//.//0 is still alive. The exact analytic results also confirm the numerical spectrum. We then develop Polnarev's analytic method to calculate of the polar-ization power spectrum of CMB generated by cosmic RGW. The ana-lytic polarization spectra have been obtained with following several im-provements over the previous results. 1. The approximate analytic re-sult of CMB polarization is quite close to the numerical one evaluated from the cmbfast code, especially, for the first three peaks of the spec-trum that are observable. By using the analytic exact solution of RGW from the sudden-change approximation, we have demonstrated the de-pendence of polarization on the dark energy and the baryon. 2. Our analytic half-gaussian approximation of the visibility function fits ana-lytically better than the usual Gaussian model, and its time integration yields a arameter-dependent damping factor. This improves the spec-trum //~// 30% around the second and third peaks. 3. The second order of tight coupling limit educes the amplitude of spectra by 58%, comparing with the first order. 4. The influence of the power spectrum index of RGW is such that a larger value of the power index //nT// produces higher polarization spectra.
 * Relic Gravitational Waves and CMB Polarization in Accelerating Universe **
 * Y. Zhang, ** W. Zhao, X.Z. Er, and T.Y. Xia
 * Astrophysics **** Center University of Science and Technology of China **
 * Hefei ****, Anhui, China **