Astronomy
Using the Cosmic Microwave Background to Constrain the Hubble Constant
Quick fact
The Planck satellite's measurement of the cosmic microwave background gives a Hubble constant of about 67.4 km/s/Mpc, which is about 8% smaller than the 73 km/s/Mpc value inferred from local distance measurements—a discrepancy known as the Hubble tension.
Why this is interesting
The oldest light in the universe carries a hidden measurement of how fast it is expanding today. But that measurement disagrees with what we see in our cosmic backyard.
Read the full explanation
Understanding Using the Cosmic Microwave Background to Constrain the Hubble Constant
The cosmic microwave background (CMB) is a faint glow of microwave radiation that fills the entire sky, emitted when the universe became transparent about 380,000 years after the Big Bang. It shows tiny temperature fluctuations—differences of about one part in 100,000—across the sky. These fluctuations correspond to regions of slightly different density in the early universe, which seeded the formation of galaxies. The fluctuations appear on many angular scales, but there is a characteristic most common scale, seen as a series of peaks in the angular power spectrum. Because these fluctuations are essentially ripples in a fluid of photons and baryons (the 'baryon-photon plasma'), they carry information about the physics of the early universe, including the total density of matter and the distance light could have traveled until that time. By comparing the observed angular size of these fluctuations to their predicted physical size, cosmologists can deduce the curvature and composition of the universe, and from that, they can derive the expansion rate today—the Hubble constant. This requires a model of the universe's history, most notably the Lambda-CDM model, which includes dark matter, dark energy, and ordinary matter.
A deeper explanation
The CMB's temperature fluctuations are the result of acoustic oscillations in the early universe. Gravity pulls matter together, while radiation pressure pushes it apart, creating sound waves in the primordial plasma. Waves that compress at the moment of recombination (when photons decouple) create peaks in the temperature anisotropy spectrum. The first peak corresponds to the mode that compressed exactly once at recombination, and its angular scale is sensitive to the geometry of the universe—if the universe is flat, the peak appears at about 1 degree. However, to extract the Hubble constant (H0), you need to know both the physical size of the sound horizon at recombination (the maximum distance a sound wave could travel by then) and the angular diameter distance to the CMB. The physical size of the sound horizon depends on the matter density, baryon density, and radiation density at that early time. Those densities also affect the contrast of the peaks in specific ways. Therefore, by fitting the full power spectrum to a model, including the Lambda-CDM model, cosmologists can determine the best-fit values of all the cosmic parameters, including H0. The Planck satellite's CMB measurements yield H0 = 67.4 ± 0.5 km/s/Mpc. This value is extremely precise because it comes from an early-universe measurement that assumes a standard model of cosmic evolution. But when the same parameter is measured using the local distance ladder (using Cepheid variables and type Ia supernovae to measure distances and redshifts of nearby galaxies), the result is about 73 km/s/Mpc, with less than 1% uncertainty. This mismatch, known as the Hubble tension, suggests that either there is a systematic error in one of the measurements, or that the standard cosmological model is incomplete—perhaps there is new physics such as early dark energy, varying fundamental constants, or additional relativistic particles. Thus, using the CMB to constrain H0 is not just a measurement, but a powerful test of our understanding of the universe.