Simple Analytical Methods for Computing the Gravity-Wave Contribution to the Cosmic Background Radiation Anisotropy

摘要

We present two simple analytical methods for computing the gravity wavecontribution to the cosmic background radiation (CBR) anisotropy ininflationary models; one method uses a time-dependent transfer function, theother method uses an approximate gravity-wave mode function which is a simplecombination of the lowest order spherical Bessel functions. We compare the CBRanisotropy tensor multipole spectrum computed using our methods with theprevious result of the highly accurate numerical method, the ``Boltzmann''method. Our time-dependent transfer function is more accurate than thetime-independent transfer function found by Turner, White, and Lidsey; however,we find that the transfer function method is only good for $l \la 120$. Usingour approximate gravity-wave mode function, we obtain much better accuracy; thetensor multipole spectrum we find differs by less than 2\% for $l \la 50$, lessthan 10\% for $l \la 120$, and less than 20\% for $l \leq 300$ from the``Boltzmann'' result. Our approximate graviton mode function should be quiteuseful in studying tensor perturbations from inflationary models.