Total Angular Momentum Method
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
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 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.
The Web-pages devoted to this work
Full HTML Version
are part of the advanced CMB theory tutorial. Readers from this series should
refer to concepts developed in
The next set in this series is
A Complete Treatment of CMB Anisotropies
and discusses CMB theory in the general Friedman-Robertson-Walker
Phys. Rev. D 56 596 (1997)