CMB Polarization
Jack Replinger
Observational Cosmology Lab
Professor Peter Timbie
University of Wisconsin-Madison
CMB Basics


The early universe was hot, dense and
opaque

Radiation was constantly absorbed
and emitted by the early charged
particles (electrons and protons)
The universe cooled as it expanded, and
became transparent

At T=3000K, there were just enough
high energy (high frequency)
photons to ionize the particles

As the temperature continued to
drop, neutral hydrogen atoms
formed, the photons could travel
without interaction

This occurred virtually
simultaneously throughout the
universe, these photons that reach
observers today compose the CMB

This occurred at 3000K due to the
1100 fold expansion of the universe
these photons have been red-shifted
such that they are detected as a
blackbody with a temperature of
2.73K
graph courtesy of http://athene.as.arizona.edu/~lclose/teaching/a202/CMB_blackbody.gif
CMB Temperature Fluctuations
largest fluctuations ~200µK
It is important to note the
large scale smoothness and
the small scale variations.
The fact that photons from
opposite sides of the universe
of have nearly identical
energies is surprising since
according to the standard big
bang model they were never
in causal contact (could have
exchanged photons /
information).
Image from courtesy of www.aip.de/~gallery/cosmology/WMAP.jpg
The size of the small scale
variations can help us
determine the geometry of
the universe.
Inflation
ctdc*(1100)
c(to-tdc)
cti
c(to-tdc)
Θ
Era:Decoupling
Pre-Inflation
Present
causally connected region in
very early universe
These regions appear 1100 times larger
on our sky because of the expansion of
the universe from decoupling to the
present. For photons to reach an
observer on earth they will have
traveled a distance of the speed of light
times
the time
interval
The small
regions
of thebetween
CMB that have
decoupling
and
the
present.
We then
the same temperature are formed
by
can
use
simple
geometry
to
determine
regions
that
could
have communicated
The size
of the
universe
increased so
the
of these
regions
on
our
sky,
after
inflation.
These
regions
have
a
fastangle
and became
so
large,
that
our
which
work
out
to
about
one
degree
for
diameter
~ the speed
of light
entire observable
universe
is times
made the
up
a
flat
universe
(this
would
be
time
between
inflation
and
of
a interval
region
that
wasangle
causally
connected
larger
for
a
close
universe
and
smaller
decoupling.
in the pre-inflation universe
for and open universe).
Inflation Solves Three
Cosmology Problems

The Horizon Problem
 Inflation explains overall
smoothness (how opposite sides of
the universe could have been in
causal contact, and thus be the
nearly the same temperature).

The Flatness Problem
 Inflation causes the universe to be
nearly flat, which is consistent with
Θ measured by the power
spectrum (at left).

The Structure Problem
 Inflation increases quantum
mechanical fluctuations to
macroscopic scales
 Temperature fluctuations from
densities
graph courtesy of http://kicp.uchicago.edu/~davemilr/ISW/wmap_p_spec.JPG
The inflation model explains these problems but does it make predictions that we can test?
(This will be explained by the end of this presentation!)
CMB Polarization


The temperature
fluctuations have been
measured by COBE and
WMAP, but we can also
study the polarization of
the light
CMB Polarization
 Can verify the WMAP
density conclusions
 Provide additional
information
Image courtesy of http://www.physics.nyu.edu/matiasz/THESIS/tqu2.jpg
Polarization:
Assumptions and Notation



ABSORPTION AND EMISSION
 Light constantly being absorbed and emitted by charged
particles, in all directions
POLARIZATION
 The incident light is randomly polarized
MODEL
 In our model four unpolarized (shown with same magnitude
electric field perpendicular directions) photons interact with
electron from four sides perpendicular to line of sight of
observer
direction to
observer
E-fields
direction of
propagation
electron
photon(s)
high energy
photon(s)
low energy
photon(s)
How to Scatter Light:
Uniform Scattering
Note that the polarization of the
scattered photon is only effected
by the strength of the E-fields
perpendicular to its direction of
propagation
How to Polarize Light:
Quadrupole Scattering
The incident photons could be
high or low energy depending on
the motion of the particles
scattering them. A particle
moving toward this central
electron will emit a photon that is
blue shifted (having a higher
frequency and thus higher
energy). A particle moving away
from this central electron will emit
a photon that is red shifted
(having a lower frequency and
thus lower energy).
The scattered light is polarized in
the direction of blue (higher
energy) electric field
overdense visualization
screen is surface of last scattering,
therefore we are interested in the
polarization of the light
propagating out of the screen
underdense visualization
Note that we have only considered
gravitational effects, in reality when
matter condenses to a certain point in
an overdense region the matter will be
forced outward due to thermal
pressure. The motion of the charged
particles will be the same as what was
just shown for an underdense region so
the polarization pattern will also be the
same. These can be distinguished from
polarization patterns due to a different
mechanism as will be discussed.
screen is surface of last scattering,
therefore we are interested in the
polarization of the light
propagating out of the screen
Gravitational Waves

Predicted by Inflation
 Inflation theory predicts that a
large scale gravitational wave
propagated across the surface of
last scattering

Example of orientation



Propagating in z-direction
Peaks compress space in xdirection
Troughs compress space in ydirection
As shown by color of the arrows, light
received by a charged particle in the
path of the gravitational wave will blue
shifted in opposite directions (high
energy), and red shifted in the
perpendicular directions (low energy).
Again we have a quadrupole, the light
scattered out of the screen will be
polarized in the direction that the oval
is compressed.
Gravitational Wave Propagating Across Surface of Last Scattering
peak
trough
Direction of Gravitational Wave:
Into Screen
Gravitational Wave Propagating Across Surface of Last Scattering
View of Cross Section
Since an observer on earth is at the
center of the spherical shell that makes
up the surface of last scattering this is
what we see on the sky
Direction of Gravitational Wave:
Into Screen
The gravitational wave reaches the outer
most (closest) matter of the shell first
expanding them horizontally. Then
strikes the matter on the red circle a half
wave length later. And finally the
innermost matter. Recall the polarization
is in the direction the matter is
compressed.
E-modes

Polarizations due to densities (or thermal pressure) have gradient, are known as E-modes
B-modes

Polarizations due to gravitational waves are the only source of curl, are known as B-modes
MBI

The Observational Cosmology Lab at
UW-Madison
 Headed by Professor Peter Timbie
 Current project: Millimeterwave Bolometric
Interferometer (MBI)



Procedure: measure the polarization of the CMB
Data: look for E-modes and B-modes
Purpose: Better understand the origins of our
universe.