Introduction to Microwave Background Polarization

Microwave background polarization, though presently undetected, is a fundamental prediction of any viable cosmological model. These lectures review the theoretical description of polarization, its physical interpretation, and potentially interesting polarization signals.Comment: Lectures given at the International School of Space Sciences, L'Aquila, Italy, September 2-12, 1998. 18 pages with 2 figures; Elsevier tex macro

Cosmic Microwave Background Polarization

Polarization of the cosmic microwave background, though not yet detected, provides a source of information about cosmological parameters complementary to temperature fluctuations. This paper provides a complete theoretical treatment of polarization fluctuations. After a discussion of the physics of polarization, the Boltzmann equation governing the evolution of the photon density matrix is derived from quantum theory and applied to microwave background fluctuations, resulting in a complete set of transport equations for the Stokes parameters from both scalar and tensor metric perturbations. This approach is equivalent at lowest order in scattering kinematics to classical radiative transfer, and provides a general framework for treating the cosmological evolution of density matrices. The metric perturbations are treated in the physically appealing longitudinal gauge. Expressions for various temperature and polarization correlation functions are derived. Detection prospects and theoretical utility of microwave background polarization are briefly discussed.Comment: Replaced version corrects factor of 2 error in the Liouville equation. 24 pages, Postscrip

The Signature of Proper Motion in the Microwave Sky

The cosmic microwave background radiation defines a preferred cosmic rest frame, and inflationary cosmological theories predict that the microwave background temperature fluctuations should be statistically isotropic in this rest frame. For observers moving with respect to the rest frame, the temperature fluctuations will no longer be isotropic, due to the preferred direction of motion. The most prominent effect is a dipole temperature variation, which has long been observed with an amplitude of a part in a thousand of the mean temperature. An observer's velocity with respect to the rest frame will also induce changes in the angular correlation function and creation of non-zero off-diagonal correlations between multipole moments. We calculate both of these effects, which are part-in-a-thousand corrections to the rest frame power spectrum and correlation function. Both should be detectable in future full-sky microwave maps from the Planck satellite. These signals will constrain cosmological models in which the cosmic dipole arises partly from large-scale isocurvature perturbations, as suggested by recent observations.Comment: 5 pages, no figures. Submitted to Physical Review Letter

Efficient Cosmological Parameter Estimation from Microwave Background Anisotropies

We revisit the issue of cosmological parameter estimation in light of current and upcoming high-precision measurements of the cosmic microwave background power spectrum. Physical quantities which determine the power spectrum are reviewed, and their connection to familiar cosmological parameters is explicated. We present a set of physical parameters, analytic functions of the usual cosmological parameters, upon which the microwave background power spectrum depends linearly (or with some other simple dependence) over a wide range of parameter values. With such a set of parameters, microwave background power spectra can be estimated with high accuracy and negligible computational effort, vastly increasing the efficiency of cosmological parameter error determination. The techniques presented here allow calculation of microwave background power spectra $10^5$ times faster than comparably accurate direct codes (after precomputing a handful of power spectra). We discuss various issues of parameter estimation, including parameter degeneracies, numerical precision, mapping between physical and cosmological parameters, and systematic errors, and illustrate these considerations with an idealized model of the MAP experiment.Comment: 22 pages, 12 figure

CMBFAST for spatially closed universes

We extend the cosmological linear perturbation theory code CMBFAST to closed geometries. This completes the implementation of CMBFAST to all types of geometries and allows the user to perform an unlimited search in the parameter space of models. This will be specially useful for placing confidence limits on cosmological parameters from existing and future data. We discuss some of the technical issues regarding the implementation.Comment: 6 pages, 2 figures, new version of CMBFAST can be found http://www.sns.ias.edu/~matiasz/CMBFAST/cmbfast.htm