Cosmic Microwave
Background Polarization:
The Next Key Toward the Origin of the Universe
Since the 1960s, humans on Earth have been able to study the cosmic
microwave background (CMB) radiation left over from the Big Bang 14
billion years ago. The observed pattern of the CMB intensity across
the sky has told us much about our
universe, including its history, age, geometry, density,.... However, we
still know very little, especially about the earliest moments of the
Creation. We can learn about the first fraction of a second, among other
things, by studying the polarization pattern of the CMB...
1. How did the Universe Begin? Inflation?
Currently the best theory we have about the earliest moment in the
history of the universe is called "Inflation".
During a tiny fraction of a second after the Big Bang, the universe
seeems to have expanded exponentially, much faster than usual. This
scenario explains several important observations about the universe:
- Why the universe appears to have no overall curvature (flat).
- Why the universe appears so isotropic.
- Why there are structures in the universe.
- Why we have not found cosmic relics like the magnetic monopoles.
Even though inflation conveniently explains these mysteries, we have no
direct evidence that inflation is really what happened.
|
Guth
|
Did inflation happen?
How fast did the universe expand?
How can we explain inflation?
The explosive expansion of space during inflation would have created
ripples in the fabric of space. As explained below, these gravity waves
should have left a signature in the polarization of the last-scattered
photons (CMB).
Kamionkowski
The amplitude of the gravity wave is proportional to the expansion rate
H during inflation, which in turn is proportional to the inflation
energy scale squared:
GW amplitude ∝ H ∝ Einf2, where
Einf~<1016GeV
But how did gravity waves cause CMB polarization?
The CMB radiation is polarized because it was scattered off of free
electrons during decoupling.
| colder radiation ↓ |
| hotter radiation → |
Hu 2001 |
When an electromagentic wave is incident on a free electron, the
scattered wave is polarized perpendicular to the incidence direction.
If the incident radiation were isotropic or had only a dipole variation,
the scattered radiation would have no net polarization.
However, if the incident radiation from perpendicular directions
(separated by 90°) had different intensities, a net linear
polarization would result. Such anisotropy is called "quadrupole" because
the poles of anisotropy are 360°/4 = 90° apart.
But why was there quadrupole anisotropy? |
At radiation decoupling when photons last scattered off of electrons,
there was temperature inhomogeneity (shown in the animation as a pattern
of red and blue). When recombination proceeded to the point where photons
from hot and cold regions could meet to be scattered by the same electron,
the scattered radiation were polarized. For
example, for an electron at the center of the middle circle, photons
(yellow) diffusing from vertical directions are hotter (blue) while
photons from horizontal directions are colder (red). Comparing this
situation with the above animation, the net polarization of the scattered
radiation is horizontal (green line).
This photon diffusion into regions of different temperatures were
possible only when the plasma became optically thin enough during
recombination. Also, these diffused photons could scatter only
while there are still free electrons left. Thus, polarized radiation
could be produced only during a short period near the end of
recombination. Only a small fraction of the CMB radiation is therefore
polarized.
Electrons at different locations (at the center of different rings
in the animation) would produce different polarization orientations and
magnitudes. As observed today, the CMB polarization varies across the
sky. The quadrupole anisotropies at decoupling are projected into CMB
polarization pattern. Since photons could not diffuse too far,
polarization doesn't vary much across very large angular scales.
What else could cause quadrupole anisotropy?
The quadrupole anisotropy (which produced CMB polarization) could arise
from 3 types of perturbations:
- Scalar (due to density fluctuations)
- Vector (due to vorticity induced by defects/strings)
- Tensor (due to gravity waves)
Hu 2001
Scalar perturbation: Energy density fluctuations in the
plasma (resulting in hotter and colder regions) cause velocity
distributions that are out of phase with the acoustic density mode. The
fluid velocity from hot to colder regions cause blueshift of the photons,
resulting in quadrupole anisotropy.
Vector perturbation: Vorticity in the plasma cause
Doppler shifts resulting in the quadrupole lobes in the figure. However,
vorticity would be damped by inflation and is expected to be negligible.
Tensor perturbation: Gravity waves stretch and squeeze
space in orthogonal directions (as shown by the test 'circles' in the
figure). This also stretches the wavelength of radiation, therefore
creating quadrupole variation in incoming radiation temperature. Gravity
waves from inflation would produce tensor perturbation!
The polarization pattern in the sky can be decomposed into 2 components:
- Curl-free component, called "E-mode" (electric-field like) or
"gradient-mode", with no handedness
- Grad-free component, called "B-mode" (magnetic-field like) or
"curl-mode", with handedness
The E-mode may be due to both the scalar and tensor perturbations, but
the B-mode is due to only vector or tensor perturbations because of their
handedness.
| E-mode: | G (grad)
| no-handed |
<= Scalar / Tensor perturbations |
| B-mode: | C (curl)
| handed |
<= Vector / Tensor perturbations |
7. Polarization Anisotropy Spectrum
Once we have maps of the E- and B- components (and the temperature
anisotropy), we can analyze them by decomposing them in terms of spherical
harmonics. For example, for temperature anisotropy Θ ≡
ΔT/T:
Since the E- and B- polarization modes come from different physics, the
anisotropy spectra for the two components are expected to have different
shapes and amplitudes.
Hu et al 2003