An Analytic Approach to the Polarization of the Cosmic Microwave Background Generated by Relic Gravitational Waves

We develop the Polnarev’s analytic method to calculate of the polarization power spectrum of the cosmic microwave background radiation (CMB) due to relic gravitational waves. This approach complements the more precise numerical results by providing insight into the physical origins of the features in the power spectrum. We make use of the WKB approach to handle the evolution of the relic gravitational waves during the transition from the radiation-dominated to the matter-dominated Universe. To better describe the decoupling history of the Universe, we use a half-gaussian function to approximate the visibility function. At last, we give an expression of the power spectrum of CMB, which is generated by the relic gravitational waves. It illustrates the dependence of the amplitude, shape, and peak locations on the details of recombination, the gravitational-wave power spectrum, and the cosmological parameters. PACS numbers: 98.80.-k, 98.80.Es, 04.30.-w, 04.62+v,