A Fast and Accurate Algorithm for Computing Tensor CBR Anisotropy

Inflation gives rise to a nearly scale-invariant spectrum of tensor perturbations (gravitational waves), their contribution to the Cosmic Background Radiation (CBR) anisotropy depends upon the present cosmological parameters as well as inflationary parameters. The analysis of a sampling-variance-limited CBR map offers the most promising means of detecting tensor perturbations, but will require evaluation of the predicted multipole spectrum for a very large number of cosmological parameter sets. We present accurate polynomial formulae for computing the predicted variance of the multipole moments in terms of the cosmological parameters ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$, ${\mathrm{\Omega }}_0{h}^2$, ${\mathrm{\Omega }}_B{h}^2$, $N_{\nu }$, and the power-law index $n_T$ which are accurate to about 1% for $l\le 50$ and to better than 3% for $50< l \le 100$ (as compared to the numerical results of a Boltzmann code).