13.2 Cosmic microwave background radiation

Discovery and Properties of the CMB

The cosmic microwave background (CMB) is a faint glow of microwave radiation that fills the entire universe in every direction. It's the oldest light we can observe, released about 380,000 years after the Big Bang when the universe cooled enough for atoms to form and photons to travel freely. The CMB serves as one of the strongest pieces of evidence for the Big Bang theory and gives us a direct snapshot of conditions in the early universe.

CMB data reveals tiny temperature fluctuations across the sky that turn out to be extraordinarily informative. These fluctuations encode information about the universe's composition, age, and geometry, making the CMB arguably the single most important observable in modern cosmology.

Discovery of the CMB

In 1964, Arno Penzias and Robert Wilson were working with the Holmdel Horn Antenna at Bell Labs in New Jersey, calibrating it for satellite communication experiments. They detected a persistent background noise in their radio signals that they couldn't eliminate. After ruling out every possible source of interference (including pigeon droppings in the antenna), they realized the noise was real: uniform microwave radiation arriving from every direction in the sky.

At the same time, a group of physicists at nearby Princeton (led by Robert Dicke) had been independently predicting that a remnant glow from the Big Bang should be detectable as microwave radiation. When the two groups connected, it became clear that Penzias and Wilson had found exactly what the Princeton team predicted. This discovery earned Penzias and Wilson the 1978 Nobel Prize in Physics.

CMB as Evidence for the Big Bang

The CMB supports the Big Bang theory in several reinforcing ways:

• Isotropy. The radiation is remarkably uniform across the entire sky, consistent with an expanding universe that originated from a hot, dense state where everything was in thermal equilibrium.
• Perfect blackbody spectrum. The CMB follows a blackbody curve almost exactly, peaking at a temperature of approximately 2.725 Kelvin. This is precisely what you'd expect from thermal radiation that has been redshifted by billions of years of cosmic expansion. The COBE satellite measured this spectrum in 1990, and it matched the theoretical blackbody curve so well that the error bars were smaller than the thickness of the plotted line.
• Predicted temperature. Early Big Bang models predicted that the universe should have cooled to a few Kelvin by now. The measured $T \approx 2.725 \, \text{K}$ matches those predictions.
• Consistency with nucleosynthesis. CMB observations support Big Bang nucleosynthesis predictions for the abundances of light elements (hydrogen, helium, and lithium) produced in the first few minutes after the Big Bang.
• Age constraint. CMB data, combined with other measurements, constrains the age of the universe to about 13.8 billion years.

Significance of CMB Temperature Fluctuations

While the CMB is remarkably uniform, it's not perfectly so. Tiny temperature variations exist across the sky, on the order of about 1 part in 100,000 (roughly $\pm 200 \, \mu\text{K}$). These anisotropies are small, but they carry an enormous amount of information.

Where the fluctuations come from:

• Quantum fluctuations in the very early universe (possibly amplified during inflation) created slight density variations in the primordial plasma.
• These density variations drove acoustic oscillations: pressure waves in the hot plasma of photons and baryons before recombination. Regions of higher density were slightly hotter; regions of lower density were slightly cooler.

Why they matter:

• These fluctuations are the seeds of all cosmic structure. The slightly overdense regions eventually grew through gravitational attraction into the galaxies and galaxy clusters we see today.
• The angular scale of the fluctuations on the sky is directly related to the physical size of the universe at the time of recombination (about 380,000 years after the Big Bang).
• The CMB power spectrum plots the intensity of fluctuations at different angular scales. Its peaks and troughs correspond to distinct physical processes: the first peak reflects the fundamental acoustic oscillation mode, higher peaks encode information about baryon loading, and damping at small scales (called Silk damping) reveals the diffusion of photons in the early plasma.

CMB and Cosmological Parameters

The CMB power spectrum is remarkably sensitive to the fundamental parameters of the universe. By fitting models to the observed peak structure, cosmologists can extract precise values for several quantities:

• Geometry of the universe. The angular position of the first acoustic peak indicates that the universe is very close to spatially flat (zero curvature), consistent with $\Omega_{\text{total}} \approx 1$.
• Baryon density. The relative heights of the odd and even acoustic peaks reveal the fraction of the universe made of ordinary (baryonic) matter, roughly 5% of the total energy density.
• Dark matter density. The overall shape and peak ratios of the power spectrum constrain the dark matter content to about 27% of the total energy density.
• Dark energy. CMB data alone provides some constraints on dark energy, but combining it with other observations (Type Ia supernovae, baryon acoustic oscillations in galaxy surveys) tightens these constraints significantly.
• Hubble constant. CMB measurements provide an independent estimate of $H_0$, the current expansion rate. Notably, the CMB-derived value (around 67.4 km/s/Mpc from Planck) sits in some tension with local distance-ladder measurements (around 73 km/s/Mpc), a discrepancy that remains an active area of research.
• Support for inflation. The near-flatness of the universe, the superhorizon correlations in the CMB, and the nearly scale-invariant spectrum of fluctuations all support inflationary models, which propose a brief period of exponential expansion in the universe's first fraction of a second.