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# CMB ANISOTROPIES: TOTAL ANGULAR MOMENTUM METHOD

**Wayne Hu**^{1} &
Martin White^{2}

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

Princeton, NJ 08540

^{2}Enrico Fermi Institute, University of Chicago

Chicago, IL 60637

### Abstract:

A total angular momentum representation simplifies the radiation
transport problem for temperature and polarization anisotropy in
the CMB. Scattering terms couple only the quadrupole moments of the
distributions and each moment corresponds directly to the
observable angular pattern on the sky. We develop and employ
these techniques to study the general properties of anisotropy
generation from scalar, vector and tensor perturbations to the
metric and the matter, both in the cosmological fluids and
from any seed perturbations (e.g. defects) that may be present.
The simpler, more transparent form and derivation of the Boltzmann
equations brings out the geometric and model-independent aspects of
temperature and polarization anisotropy formation. Large angle
scalar polarization provides a robust means to distinguish between
isocurvature and adiabatic models for structure formation in principle.
Vector modes have the unique property that the CMB polarization
is dominated by magnetic type parity at small angles (a factor
of 6 in power compared with for the scalars and 8/13
for the tensors) and hence potentially distinguishable independent of
the model for the seed. The tensor modes produce a different sign
from the scalars and vectors for the temperature-polarization
correlations at large angles. We explore conditions under which one
perturbation type may dominate over the others including a
detailed treatment of the photon-baryon fluid before recombination.

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*Wayne Hu*

*9/9/1997*