Wayne Hu1, Uros Seljak2, Martin White3, & Matias Zaldarriaga4
1 Institute for Advanced Study, School of Natural Sciences,
Princeton, NJ 08540
2 Harvard Smithsonian Center For Astrophysics, Cambridge, MA 02138
3Departments of Physics and Astronomy, University of Illinois at Urbana-Champaign, Urbana, IL 61801
4 Department of Physics, MIT, Cambridge, MA 02139
We generalize the total angular momentum method for computing Cosmic Microwave Background anisotropies to Friedman-Robertson-Walker (FRW) spaces with arbitrary geometries. This unifies the treatment of temperature and polarization anisotropies generated by scalar, vector and tensor perturbations of the fluid, seed, or a scalar field, in a universe with constant comoving curvature. The resulting formalism generalizes and simplifies the calculation of anisotropies and, in its integral form, allows for a fast calculation of model predictions in linear theory for any FRW metric. With this work, the perturbation theory of CMB temperature and polarization anisotropy formation through gravitational instability in an FRW universe may be considered complete.