Simple analytical methods for computing the gravity-wave contribution to the cosmic background radiation anisotropy

We present two simple analytical methods for computing the gravity-wave contribution to the cosmic background radiation (CBR) anisotropy in inflationary models; one method uses a time-dependent transfer function, the other methods uses an approximate gravity-mode function which is a simple combination of the lowest order spherical Bessel functions. We compare the CBR anisotropy tensor multipole spectrum computed using our methods with the previous result of the highly accurate numerical method, the ``Boltzmann'' method. Our time-dependent transfer function is more accurate than the time-independent transfer function found by Turner, White, and Lindsey; however, we find that the transfer function method is only good for l<~120. Using our approximate gravity-wave mode function, we obtain much better accuracy; the tensor multipole spectrum we find differs by less than 2% for l<~50, less than 10% for l<~120, and less than 20% for l<=300 from the ``Boltzmann'' result. Our approximate graviton mode function should be quite useful in studying tensor perturbations from inflationary models.