Cosmic microwave background

The cosmic microwave background (CMB) is a faint electromagnetic radiation that permeates the entire universe. It is a relic of the hot, dense, and nearly uniform state in which the universe began about 13.8 billion years ago. Released when the universe had cooled enough to become transparent, a few hundred thousand years after the Big Bang, it is the oldest light that can be observed today.

Because the expansion of the universe has stretched the photons of the cosmic microwave background by a factor of about 1100, the radiation is observed today not as visible light but as microwaves, forming a near-perfect blackbody at a temperature of about 2.7 kelvin.

The existence of CMB was predicted in the 1940s as a necessary consequence of the Big Bang. The first observation, by accident, was in 1965 by Arno Penzias and Robert Woodrow Wilson, two radio astronomers at Bell Telephone Laboratories, while they were trying to minimise noise for their ultra-sensitive satelite communication ground receiver. They were awarded the 1978 Nobel Prize in Physics for the detection.

Because the spectrum and spatial pattern of CMB can be measured with exquisite precision, it has become the single most informative observable in cosmology. Although its temperature is almost perfectly uniform across space, tiny variations by about 10 ppm encodes the geometry, composition, age and history of the universe. It is the strongest evidence that the universe is spatially flat, and it anchors the measurement of the abundance of ordinary matter, dark matter and dark energy.

History

Prediction

In the 1940s, George Gamow and his collaborators demonstrated that if the universe began in an enormously hot and dense state as suggested by the Big Bang theory, it should still be filled with the radiation left over from that era. Ralph Asher Alpher and Robert Herman further estimated that taking into account the cooling provided by an expanding universe, the temperature of this relic radiation should be only a few kelvins. The prediction attracted little attention at the time, and the observation of the radiation was not actively searched for.

Accidental discovery (1964–1965)

In the early 1960s, a group of physicists led by Robert H. Dicke at Princeton University revisisted the idea. They began building a small radiometer to look for CMB at a wavelength of about 3 centimetres. Their progress, however, was superceded by a couple of telecommunication engineers that were not looking for CMB at all.

The Holmdel horn antenna at Bell Telephone Laboratories in New Jersey, with which Penzias and Wilson discovered the cosmic microwave background in 1965. Credit: Erik Dunham (CC BY-SA 3.0).

In 1964 and 1965, Arno Penzias and Robert Woodrow Wilson were using a 20-foot horn-reflector antenna in Holmdel, New Jersey, built for satellite communications, to measure the faint radio emission of the Milky Way. At a wavelength of 7.35 centimetres (a frequency of 4080 megacycles per second), they found an excess antenna temperature of about 3.5 kelvin that was isotropic, unpolarised, and present at all times of day and year, whatever part of the sky the antenna pointed at. They eliminated every source of noise they could think of, even removing a pair of pigeons that had taken up residence in the antenna throat and cleaning away the "white dielectric material" they had left behind, yet the excess remained.

Penzias and Wilson reported the measurement in a short paper, "A Measurement of Excess Antenna Temperature at 4080 Mc/s", published in 1965 in The Astrophysical Journal. Almost simultaneously, and in the same issue of the journal, Dicke's group published the companion paper interpreting the excess as the relic radiation of the Big Bang, which they had been about to search for. The two groups had been in contact: when Dicke heard of the Bell Labs result, he is said to have told his colleagues, "Well, boys, we've been scooped." The radiation became known as the cosmic microwave background.

Arno Penzias and Robert Woodrow Wilson shared the 1978 Nobel Prize in Physics for their discovery.

COBE: the spectrum and the fluctuations

In 1989, NASA launched its Cosmic Background Explorer (COBE) satellite. It carried three instruments dedicated to study the radiation of CMB:

• The Far-Infrared Absolute Spectrophotometer (FIRAS),
• The Differential Microwave Radiometer (DMR)

significant conclusions were obtained through the analysis of data collected by COBE. A team led by John C. Mather, compared  with an internal blackbody calibrator and showed that its spectrum corresponds to near-perfect blackbody, with any deviations from a perfect blackbody limited to about 50ppm of the peak brightness. Another team, led by George F. Smoot, discovered spatial temperature fluctuations at the level of about 10 ppm.

The COBE results transformed the study of the CMB: the measurement of a near-perfect blackbody spectrum confirmed that the radiation is a relic of a hot, dense, thermalised early universe, while the detection of fluctuations showed that the early universe was not perfectly smooth, providing the seeds from which galaxies and clusters later grew.

John C. Mather and George F. Smoot shared the 2006 Nobel Prize in Physics for these measurements.

WMAP and Planck

The evolution of CMB maps: COBE (left, 1989), WMAP (centre, 2001) and Planck (right, 2009). Each generation resolved the temperature pattern with greater sensitivity. Credit: NASA/JPL-Caltech/ESA (public domain).

Two subsequent space missions, NASA's Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001, and ESA's Planck satellite, launched in 2009, mapped the temperature and polarisation of the CMB across the whole sky with far higher sensitivity and resolution compared to the COBE results, providing precious data to determine with high precision the age of the universe and to estimate the cosmological constant.

Origin and physical properties

The surface of last scattering

In the hot early universe, matter was ionised: free protons and electrons formed a plasma that scattered light almost continuously, so that radiation and matter were tightly coupled and the universe was opaque. As the universe expanded, it cooled, until, a few hundred thousand years after the Big Bang, its temperature had fallen to about 3000 kelvin and the free electrons combined with protons to form neutral hydrogen, in the epoch known as recombination. With the charged particles gone, the radiation was suddenly free to travel: the universe became transparent, and the photons that had been scattered for the last time began to stream freely. Those photons are the cosmic microwave background we observe today.

The region from which these photons reach us is called the surface of last scattering. It is not a physical surface but a spherical shell centred on the observer, at a redshift of about 1090, corresponding to a time when the universe was about 380,000 years old and roughly one-thousandth of its present size. Since decoupling, the expansion of the universe has stretched the wavelength of each photon by a factor of (1 + z), so that the temperature of the radiation scales with redshift as

T(z) = T_{0}(1 + z)

where T₀ ≈ 2.7 K is the temperature measured today. Between emission and reception, the CMB photons have travelled almost freely, deflected only slightly by the gravity of intervening matter, an effect known as gravitational lensing.

A near-perfect blackbody

The spectrum of the cosmic microwave background measured by the FIRAS instrument on COBE (points) compared with the theoretical curve of a single-temperature blackbody (solid line); the error bars are too small to be seen. Credit: plot of public-domain NASA COBE data (public domain).

A blackbody is an ideal emitter that radiates purely according to its temperature. The spectrum of the cosmic microwave background matches the Planck function, the theoretical spectrum of a blackbody, to extraordinary precision: FIRAS measured it across more than a decade of the spectrum and found the data to be indistinguishable from a blackbody curve, placing tight limits on any deviation. In terms of frequency ν, the intensity of a blackbody at temperature T is given by Planck's law:

B_{\nu}(T) = \frac{2h\nu^{3}}{c^{2}}\frac{1}{e^{h\nu/k_{\mathrm{B}}T} - 1}

where h is the Planck constant, c the speed of light, and k_B the Boltzmann constant. The temperature of the CMB monopole, the sky-averaged value of the radiation, is about 2.7 K, and its spectrum peaks at a wavelength set by Wien's displacement law:

\lambda_{\mathrm{max}}T = b, \quad b \approx 2.898\times10^{-3}\,\mathrm{m\,K}

For T ≈ 2.7 K this gives a peak wavelength of roughly a millimetre, squarely in the microwave band, which is why the radiation is observed with microwave instruments.

That the CMB is such a precise blackbody is powerful evidence for the hot Big Bang theory. Only radiation that was once in thermal equilibrium with matter in an extremely hot, dense phase can plausibly fill the sky with a blackbody spectrum to this accuracy; steady-state cosmologies, in which the radiation would have to be produced by astrophysical sources, have no natural way of generating it.

A geometric probe of the universe

The history of the universe from the Big Bang to the present. The cosmic microwave background was released at recombination, a few hundred thousand years after the Big Bang (right of centre). Credit: NASA/WMAP Science Team (public domain).

The pattern of the CMB also makes it a precise probe of the geometry of the universe. Cosmologists describe densities in terms of the critical density, the density that would just halt the expansion of a spatially flat universe:

\rho_c = \frac{3 H^2}{8 \pi G}

where H is the Hubble parameter and G the gravitational constant. The ratio of any component's density to the critical density is its density parameter, and the total density parameter of the universe is usually written Ω_total. The angular scale of the acoustic peaks of the CMB (described below) depends on the total density: in a positively curved universe, features would appear larger than in a flat one, and in a negatively curved universe they would appear smaller. The Planck measurements of the peaks imply a total density parameter of 1 to within a few tenths of a percent, and a curvature density parameter Ω_K = 0.0007 ± 0.0019: the universe is spatially flat to very high precision.

Flatness alone does not fix the composition, but the detailed shape of the CMB pattern does. Planck finds that ordinary baryonic matter contributes about 5% of the total density, dark matter about 27%, and dark energy about 68%, with the dark energy behaving like a cosmological constant. These are the values quoted in the articles on dark energy and dark matter, which the CMB constrains jointly with the other cosmological probes.

The anisotropy of the CMB

The dipole

All-sky map of the cosmic microwave background measured by ESA's Planck satellite. The colour differences are temperature fluctuations of about one part in 100,000. Credit: ESA and the Planck Collaboration (CC BY 4.0).

The largest apparent departure from uniformity of the CMB is a dipole: the sky is very slightly hotter in one direction and colder in the opposite one, by about one part in a thousand, a temperature difference of a few millikelvin. The dipole does not originate in the early universe but in our own motion: the Solar System is moving at a few hundred kilometres per second relative to the rest frame defined by the CMB, and the resulting Doppler shift makes the radiation slightly hotter in the direction of motion and colder behind us. Removing this dipole is the first step in analysing the CMB, and it leaves a pattern that is uniform to one part in 100,000.

Fluctuations of one part in 100,000

After the dipole is subtracted, the CMB temperature is almost perfectly constant across the sky: the remaining fluctuations, first detected by COBE in 1992, are at the level of about 30 microkelvin, one part in 100,000 of the mean. These fluctuations are the imprint of tiny density variations present in the universe at recombination, the "seeds" from which galaxies, clusters and the large-scale structure of the cosmos later grew by gravitational instability: slightly overdense regions had slightly hotter radiation and eventually collapsed into the structures seen today.

The pattern of the fluctuations is nearly scale-invariant, meaning that patches of very different angular size have comparable amplitude, as predicted by the theory of cosmic inflation. The statistics of the pattern are described by expanding the temperature map into spherical harmonics, each labelled by a multipole ℓ that roughly corresponds to an angular scale of 180°/ℓ.

The angular power spectrum

The angular power spectrum of the CMB temperature anisotropies from three years of WMAP data (points) together with measurements from ground-based and balloon-borne experiments (coloured points); the solid curve is the best-fitting cosmological model. Credit: NASA/WMAP Science Team (public domain).

The statistical content of the fluctuations is usually summarised by the angular power spectrum, the variance of the spherical-harmonic coefficients C_ℓ as a function of multipole ℓ, conventionally plotted in the dimensionless form

\mathcal{D}_{\ell} = \frac{\ell(\ell+1)}{2\pi}C_{\ell}

The power spectrum of the CMB is not flat: it shows a series of peaks and troughs, the acoustic peaks, which are among the most important measurements in cosmology. They arise because, before recombination, the photon–baryon fluid supported sound waves: gravity compressed overdense regions while radiation pressure pushed back, setting up oscillations that froze into the temperature pattern when the radiation decoupled. Modes that had completed a whole number of half-oscillations by decoupling appear as peaks in the power spectrum, and modes caught at other phases appear as troughs.

Each feature of the power spectrum carries specific information:

• the position of the first peak, at ℓ ≈ 200, is set by the angular size of the sound horizon and measures the total density of the universe, pinning down its geometry;
• the odd–even alternation in the heights of successive peaks, the pattern of compressional versus rarefactional modes, measures the baryon density, since baryons load the compressional modes;
• the overall damping of the peaks at high ℓ, caused by photons diffusing out of small regions during recombination (Silk damping), measures the matter density and the thickness of the last scattering surface;
• the plateau of power at low ℓ, the Sachs–Wolfe effect, reflects the gravitational potential fluctuations and measures the amplitude and tilt of the primordial fluctuation spectrum;
• gravitational lensing of the CMB by intervening matter slightly smooths the peaks and adds power at small scales, providing a direct measurement of the growth of structure, sensitive to dark matter.

Fitting the full spectrum together with the polarisation measurements and the lensing signal yields the parameters of the standard model of cosmology, and it is in this way that the CMB constrains the geometry, contents and age of the universe quoted above.

Polarisation

The CMB is also faintly polarised, at the level of a few microkelvin, because the last scattering of the photons was not isotropic: the quadrupolar pattern of the incoming radiation around each scattering electron imprinted a preferred direction on the scattered light. The polarisation pattern can be decomposed into a curl-free component (E-modes), generated by the same density fluctuations that produce the temperature anisotropies, and a divergence-free component (B-modes), which density fluctuations cannot generate at first order.

A primordial B-mode signal would be the signature of gravitational waves generated during cosmic inflation, stretched to cosmological scales by the rapid expansion. Its detection would directly probe the energy scale of inflation. So far, searches combining Planck data with ground-based and balloon-borne experiments such as BICEP/Keck have found no convincing primordial B-mode signal, and instead measure the E-mode pattern precisely and the lensing-induced B-modes, continuing to tighten the constraints on the standard model.

Further reading

• The Universe, NASA Science
• Wilkinson Microwave Anisotropy Probe, NASA
• Planck, European Space Agency
• Planck 2018 results. VI. Cosmological parameters, Planck Collaboration (2020)