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...
|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:
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:
But how did gravity waves cause CMB polarization?
|colder radiation ↓|
|hotter radiation →||
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 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:
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|
Seljak & Zaldarriaga
↑ pure E-mode pure B-mode ↑
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:
|The multipole moments are used to define the power spectra:
(The B-mode is not expected to correlate with E or Θ because of its handedness.)
Each of these can be scaled to give a corresponding magnitude in temperature scale: =>
The upper curve (black) is the most familiar temperature anisotropy spectrum, with amplitudes 5 orders of magnitude smaller than the CMB temperature of 3 K.
The polarization signals (EE,BB) are smaller by an additional 1~2 orders of magnitude because the polarized radiation were produced only near the end of recombination. The polarization spectra decline at large angular scales (low l) because photons couldn't diffuse so far before the end of recombination.
(The multipole index l corresponds to angular scales of 180° / l.)
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.
|Since the velocity gradients in the plasma (which is out of phase with the density fluctuations) produced the E-mode polarization, the polarization spectrum is directly out of phase with the temperature anistropy spectrum. These two spectra are therefore correlated (TE correlation). The E-mode peaks around an angular scale corresponding to the photon mean free path at decoupling.|
|The E-mode was first detected in 2002 by DASI!
The signal level was consistent with the prediction based on the measured temperature anisotropy.
|TE correlation was measured by WMAP, matching the predicted
spectrum and showing the reionization signature!
Re-scattering of the CMB photons during reionization added to the polarization spectrum at large angular scales (l < 10). The observation indicates that reionization happened at redshift around zr = 11~30.
The most profound will be the detection of B-mode polarization due to gravity waves from the inflation at the beginning of the universe.
Based on the WMAP data, all we know is that the energy scale of inflation must have been < 3x1016 GeV (Kaplinghat 2003). When we detect the gravity wave signal, we will be able to find the energy scale of the very first major event only 10-35 second after the Creation of our universe.