Contrary to most of the Astronomy field that uses the Stokes parameters Q and U to describe their polarization measurements, in the CMB field we make use of two scalar fields E and B that are independent of how the coordinate system is oriented, and are related to the tensor field (Q,U) by a non-local transformation. Scalar CMB fluctuations have been shown to generate only E-fluctuations, whereas gravity waves, CMB lensing and foregrounds generate both E and B.
Projects:
BOOMERanG results
The Cosmic Microwave Background and Its Polarization
The Large-Scale Polarization of the Microwave Background and Foreground
Data Analysis of the POLAR Experiment
E/B Decomposition of CMB Maps
First attempt at measuring the CMB cross-polarization
A Limit on the Large Angular Scale Polarization of the CMB
How to measure CMB polarization power spectra without losing information
Resorces:
Polarization Movies
In MacTavish et al.(2006),
we present the cosmological parameters from the CMB intensity and polarization
power spectra of the 2003 Antarctic flight of the BOOMERanG telescope.
The BOOMERanG data alone constrains the parameters of the &Lambda-CDM model
remarkably well and is consistent with constraints from a multi-experiment
combined CMB data set. We add LSS data from the 2dF and SDSS redshift
surveys to the combined CMB data set and test several extensions to the
standard model including: running of the spectral index, curvature, tensor
modes, the effect of massive neutrinos, and an effective equation of state
for dark energy. We also include an analysis of constraints to a model
which allows a CDM isocurvature admixture.
In Jones et al.(2006),
we report on observations of the Cosmic Microwave Background (CMB) obtained
during the January 2003 flight of BOOMERanG . These results are derived from
195 hours of observation with four 145 GHz Polarization Sensitive Bolometer
(PSB) pairs, identical in design to the four 143 GHz Planck HFI polarized
pixels. The data include 75 hours of observations distributed over 1.84% of
the sky with an additional 120 hours concentrated on the central portion of
the field, itself representing 0.22% of the full sky. From these data we derive
an estimate of the angular power spectrum of temperature fluctuations of the
CMB in 24 bands over the multipole range (50 < l < 1500). A series of features,
consistent with those expected from acoustic oscillations in the primordial
photon-baryon fluid, are clearly evident in the power spectrum, as is the
exponential damping of power on scales smaller than the photon mean free path
at the epoch of last scattering (l > 900). As a consistency check, the
collaboration has performed two fully independent analyses of the time
ordered data, which are found to be in excellent agreement.
In Montroy et al.(2006),
we report measurements of the CMB polarization power spectra from the January
2003 Antarctic flight of BOOMERanG. The primary results come from six days of
observation of a patch covering 0.22% of the sky centered near R.A. = 82.5 deg.,
Dec= -45 deg. The observations were made using four pairs of polarization
sensitive bolometers operating in bands centered at 145 GHz. Using two independent
analysis pipelines, we measure a non-zero
In Piacentini et al.(2006),
we present a measurement of the temperature-polarization angular cross power
spectrum, TE, of the Cosmic Microwave Background. The result is based on ~ 200
hours of data from 8 polarization sensitive bolometers operating at 145 GHz during
the 2003 flight of BOOMERanG. We detect a significant
Ω CDM: Increasing the density of dark matter reduces not only the temperature, but also the polarization spectra.
Neutrino Fraction: The CMB power spectrum (temperature and polarization) changes only very weakly as you replace cold dark matter by hot. This is because the neutrinos were already quite cold (nonrelativistic) the time the CMB fluctuations are formed.
Ω Λ: The cosmological constant was completely irrelevant at z>1000, when the acoustic oscillations were created. It therefore doesn't change the shape of the peaks at all - it merely shifts them sideways, since it affects the conversion from the physical scale of the wiggles (in meters) into the angular scale (in degrees, or multipole l).
Ω Curvature: Spatial curvature was completely irrelevant at z>1000, when the acoustic oscillations were created. &Omega_k therefore doesn't change the shape of the peaks at all - it merely shifts them sideways, since the conversion from the physical scale of the wiggles (in meters) into the angular scale (in degrees, or multipole l) depends on whether space is curved. If space has negative curvature (positive &Omega_k), like a Pringles potato chip or a saddle, then the angle subtended on the sky decreases, shifting the peaks to the right. If space has positive curvature, like a balloon, then the peaks shift to the left. In addition to shifting the peaks sideways, curvature also causes fluctuations in the gravitational field to decrease over time. This also has no effect in the polarization since it is a pure gravity effect that doesn't involve Thomson scattering.
Scalar Normalization: The amplitude of density fluctuations (a.k.a. "scalar" fluctuations) simply determines the overall normalization of the two power spectra.
Tensor Normalization: As you can see, gravity waves (so-called tensor fluctuations) contribute only to fairly large angular scales in the CMB power spectrum, i.e., boost the left part. These fluctuations have a unique signature in the polarized case, since they produce B-polarization. It's important to point out that B-polarization cannot be generated by density modes, thus its detection is a signature of gravity waves (which can be used to constrain inflation).
Scalar Tilt: Changing the spectral index of scalar fluctuations simply tilts the power spectra, altering the ratio of small-scale and large-scale power in all curves.
Reionization Optical Depth:
If the Universe was reionized long ago by quasars or early stars, then there is a non-zero
optical depth &tau. This means that there is a non-zero probability that a CMB photon
arriving in our detector once Thomson scattered off of a free electron, and in fact
originated from a somewhat different direction than we thought. This effect smears out
small-scale features in the CMB power spectrum (temperature and polarization), suppressing all
acoustic peaks by a constant factor exp(-&tau), while leaving the power on the largest scales
unaffected. The new last-scattering surface at low redshift also creates new
power at low l, but this is dwarfed by the Sachs-Wolfe effect in the unpolarized case.
Since the Sachs-Wolfe effect is unpolarized, this new power is much easier to see
and quantify with E-polarization. Specifically, the location of the first new peak gives the
redshift of reionization, since it reflects the horizon size at that time.