5.3 Polarization of the CMB

CMB Polarization Mechanisms and Patterns

The CMB isn't just a map of temperature fluctuations. It's also polarized, and that polarization carries information about conditions in the early universe that temperature alone can't reveal. Specifically, polarization patterns can tell us about gravitational waves from inflation, which would confirm one of the biggest ideas in modern cosmology.

How CMB Polarization Is Produced

Polarization in the CMB arises from Thomson scattering, the process where photons scatter off free electrons during the epoch of recombination. When a photon scatters off an electron, the outgoing light becomes linearly polarized perpendicular to the plane defined by the incoming and outgoing directions.

But here's the key detail: Thomson scattering only produces net polarization if the incoming radiation has a quadrupole anisotropy, meaning the photon intensity varies in a specific pattern around the electron. If the radiation were perfectly uniform from all directions, the polarization from different incoming photons would cancel out.

Two things can create this required quadrupole anisotropy:

• Density fluctuations (scalar perturbations): Variations in matter density cause photons arriving from different directions to have slightly different temperatures, producing a quadrupole pattern.
• Gravitational waves (tensor perturbations): Primordial gravitational waves from inflation stretch and squeeze spacetime itself, distorting the photon field into a quadrupole pattern. The amplitude of this effect depends directly on the energy scale of inflation.

E-mode vs. B-mode Patterns

Any polarization map of the CMB can be mathematically decomposed into two distinct components, named by analogy to electromagnetism:

• E-modes have a curl-free pattern (like an electrostatic field). They can be generated by both scalar and tensor perturbations. E-modes were first detected by the DASI experiment in 2002 and are now well-measured.
• B-modes have a divergence-free pattern (like a magnetic field). Crucially, primordial B-modes can only be generated by tensor perturbations (gravitational waves). This is what makes them so valuable: they're a direct signature of inflationary gravitational waves, with no scalar perturbation contamination.

CMB Polarization Detection and Implications

Challenges of Detection

Detecting CMB polarization, especially B-modes, is extraordinarily difficult for several reasons:

• Weak signal: The polarization amplitude is roughly 10% of the already-tiny CMB temperature anisotropies. This demands extremely sensitive detectors and long integration times.
• Foreground contamination: Galactic dust emits polarized thermal radiation, and synchrotron emission from charged particles spiraling in the Galaxy's magnetic field also produces polarized signals. Both can mimic a primordial B-mode signal, so careful foreground modeling and subtraction are essential.

The BICEP2 experiment at the South Pole illustrates these challenges well. In 2014, the BICEP2 team announced a detection of B-mode polarization, which made headlines as potential direct evidence for inflation. However, subsequent analysis incorporating dust maps from the Planck satellite showed the signal was consistent with polarized Galactic dust rather than primordial gravitational waves. This episode underscored how critical foreground removal is for B-mode science.

Planck itself provided full-sky maps of both CMB temperature and polarization, delivering precise measurements of E-mode polarization and setting upper limits on B-modes.

What B-modes Would Tell Us About Inflation

B-mode polarization from primordial gravitational waves would be the most direct evidence for inflation we could hope for. Here's why the stakes are so high:

1. Confirmation of inflation: Inflationary gravitational waves are the only known primordial source of B-modes. A confirmed detection would be strong evidence that inflation actually occurred.
2. Measuring inflation's energy scale: The amplitude of the B-mode signal is proportional to the energy scale of inflation, quantified by the tensor-to-scalar ratio $r$. A larger $r$ means inflation occurred at higher energies. Current data from Planck (2018) sets an upper limit of $r < 0.06$.
3. Discriminating between models: Different inflationary models predict different values of $r$. High-$r$ models like chaotic inflation are already ruled out by the tight upper limits. Low-$r$ models like Starobinsky ($R^2$) inflation remain viable. A precise measurement of $r$ would dramatically narrow the field of candidate models.

The search for primordial B-modes continues with next-generation experiments like CMB-S4 and LiteBIRD, which aim to push sensitivity down to $r \sim 0.001$, probing well below current limits.