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# A COMPLETE TREATMENT OF

CMB ANISOTROPIES IN A FRW UNIVERSE

**Wayne Hu**^{1}^{},
Uros Seljak^{2},
Martin White^{3}, &
Matias Zaldarriaga^{4}

^{1} Institute for Advanced Study, School of Natural Sciences,
Princeton, NJ 08540

^{2} Harvard Smithsonian Center For Astrophysics, Cambridge,
MA 02138

^{3}Departments of Physics and Astronomy, University of Illinois
at Urbana-Champaign, Urbana, IL 61801

^{4} Department of Physics, MIT, Cambridge, MA 02139

### Abstract:

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.

*Wayne Hu*

*9/9/1997*