The Cosmic Microwave Background

What is the CMB?

In the early years following the Big Bang, the universe was extremely hot and dense and filled with free charged particles. During this time, photons were unable to travel freely through space without being scattered by the charged particles via Thomson scattering. But as the universe expanded and cooled, the charged particles combined to form neutral hydrogen. At this point, about 380,000 years after the Big Bang, light was able to travel freely for the first time without being scattered. We see this ancient light today as the cosmic microwave background (CMB) filling our sky uniformly at 2.7 Kelvin. By measuring the patterns in the CMB, we can extract a huge amount of information about the conditions and evolution of the early universe.

CMB Polarization

The CMB is linearly polarized, mostly due to Thomson scattering in the presence of density perturbations. These polarization patterns can be decomposed into two components: E-modes and B-modes. This is in analogy to electrostatics, in which the electric field has a vanishing curl and the magnetic field has a vanishing divergence. The CMB is dominated by E-modes, since density perturbations only produce E-modes.

Gravitational Lensing

Through gravitational lensing, the large scale density fluctuations in the universe like galaxy clusters deflect the trajectory of CMB photons as they propagate from the surface of last scattering to us. Lensing of the CMB gives us a handle on the cosmic expansion and structure formation history. Since lensing turns E-mode to B-mode polarization, the polarization of the CMB is an excellent tracer of lensing. 

Primordial Gravitational Wave

Inflation generates tensor fluctuations in the gravitational metric, producing gravitational waves. The amplitude of the primordial gravitational waves is directly proportional to the square of the energy scale at inflation. B-mode polarizations in the CMB is a direct probe of the primordial gravitational wave. Thus detecting B-modes generated by GW is a 'smoking gun' evidence for inflation.

Constraining Cosmological Parameters

With the B-polarization power spectrum, one can reconstruct the lensing potential power spectrum, hence infer the clustering of structures. With the information from the lensing power spectrum, several cosmological parameters are much better constrained.

Total neutrino mass

Neutrinos contribute to the total dark matter content of the universe, however, unlike normal dark matter, on small scales neutrinos do not cluster due to their extremely high velocity (~150 (1eV/mν) km/s). This effect is called neutrino free-streaming. This directly alters the shape of the matter power spectrum.

Curvature

A non-flat universe has important implications for inflation and the string landscape. With the primary CMB anisotropy alone, allowing Ωm + ΩΛ to deviate from 1 introduces parameter degeneracies between H0 and ΩΚ , as shown in the figure below. The lensing spectrum can break this degeneracy, because the amount of clustering varies for different ΩΚ values given H0, which leads to different lensing spectrum amplitudes.

Dynamical dark energy

The lensing potential spectrum provides significant constraining power, on top of the primary CMB anisotropies and polarization and external distance measurements (BAO, H0), to determine the character of dark energy, whether it is a cosmological constant or a field, and whether it has a constant or varying equation of state.

Measuring r: the tensor to scalar ratio

With a well-measured B-polarization spectrum, one can separate the lensing B-modes and the primordial B-modes and infer the energy scale at which inflation happened.