The Big Bang, CMBR, Dark Matter, and Dark Energy
The Big Bang theory states that the universe began about 13.8 billion years ago in an extremely hot, dense state and has been expanding and cooling ever since; its main evidence is the expansion (Hubble’s law), the cosmic microwave background radiation (CMBR) at 2.725 K, and the observed abundances of the light elements, while dark matter (about 27 percent of the content of the universe) and dark energy (about 68 percent) are needed to explain the structure and accelerating expansion. In brief: ordinary (baryonic) matter is only about 5 percent of the universe. The CMBR is the relic of light released about 380,000 years after the Big Bang, when the universe cooled to about 3,000 K and became transparent; it has been redshifted by a factor of about 1,100 to the microwave region. The critical density for a flat universe is ρc = 3H02 ÷ 8πG ≈ 9 × 10−27 kg/m3, about 5 hydrogen atoms per cubic meter.
Cosmology is the study of the origin, evolution and structure of the universe as a whole. This guide describes the Big Bang model and its evidence, the cosmic microwave background, the composition of the universe with dark matter and dark energy, compares the epochs in a table, works through numerical examples (the temperature of the CMB, the critical density) and corrects common mistakes.
What is the Big Bang model?
If galaxies are moving apart now, they were closer together in the past. Extrapolating back, about 13.8 billion years ago, all the matter and energy in the observable universe were in an extremely hot and dense state. The “Big Bang” was not an explosion at a point in space, but the expansion of space itself, everywhere. Before about 10−43 s (the Planck time), the physics is unknown, since quantum gravity is needed. According to the standard picture, a brief period of very rapid inflation (at about 10−36 to 10−32 s) smoothed the universe and stretched quantum fluctuations into the seeds of galaxies. As the universe expanded, it cooled: quarks combined into protons and neutrons (about 10−5 s), nuclei of helium and traces of deuterium, helium-3 and lithium formed in the first three minutes (Big Bang nucleosynthesis), atoms formed at 380,000 years (recombination), and gravity gradually assembled gas into stars and galaxies, starting a few hundred million years later.
What is the evidence?
- Expansion: Hubble’s law and the redshift of galaxies.
- Cosmic microwave background: uniform black-body radiation from all directions, predicted by Gamow, Alpher and Herman in 1948, and discovered by Arno Penzias and Robert Wilson in 1965.
- Light-element abundances: nucleosynthesis predicts that about 75 percent of the ordinary matter is hydrogen and 25 percent helium-4 by mass, with 10−5 deuterium: in agreement with the observations of the oldest gas clouds, and sensitive to the density of ordinary matter.
- Large-scale structure and the evolution of galaxies: distant galaxies (seen as they were long ago) are younger and different from nearby ones.
- Olbers’ paradox: the sky is dark at night because the universe has a finite age and is expanding.
What is the cosmic microwave background?
In the early universe, matter was a hot plasma of nuclei and electrons, opaque because photons scatter off free electrons. At about 380,000 years, when the temperature fell to about 3,000 K, electrons combined with nuclei to form neutral atoms, and the universe became transparent: the photons then traveled freely. Since then, the expansion has stretched their wavelengths by a factor of 1 + z ≈ 1,100, so the radiation now has the spectrum of a black body at T = 2.725 K (peak wavelength 1.06 mm, in the microwave region). The COBE satellite (1990) showed that the spectrum is the most perfect black body known. The radiation is almost uniform, with tiny temperature variations of about 1 part in 100,000 (anisotropies), measured by COBE, WMAP and Planck, which correspond to the seeds of structure. The pattern of these fluctuations gives the age, geometry and composition of the universe: it is flat, and consists of about 5 percent ordinary matter, 27 percent dark matter and 68 percent dark energy.
What are dark matter and dark energy?
- Dark matter does not emit or absorb light, but its gravity is seen in the rotation of galaxies, the motion of galaxies in clusters, gravitational lensing and the growth of structure. Without it, galaxies would not have formed in the time available. Its nature is unknown (possibly weakly interacting massive particles, axions or other particles); it has not been detected directly in laboratories.
- Dark energy is the name for the cause of the accelerated expansion of the universe discovered in 1998 from distant type Ia supernovae that were fainter than expected. The simplest model is a cosmological constant Λ (an energy of empty space, with constant density), which was introduced by Einstein in 1917 and later discarded. It makes up about 68 percent of the energy of the universe. As the universe expands, the density of matter falls but that of dark energy stays constant, so dark energy dominates now, and the expansion is accelerating for the last 5 billion years or so.
Epochs of the universe compared
| Time after the Big Bang | Temperature | Event |
|---|---|---|
| 10−36 to 10−32 s | About 1027 K | Inflation (hypothesized) |
| About 10−5 s | About 1012 K | Quarks form protons and neutrons |
| 3 minutes | About 109 K | Nucleosynthesis: helium forms |
| 380,000 years | About 3,000 K | Atoms form, light is released (CMBR) |
| 0.2 to 1 billion years | Cooling | First stars and galaxies |
| 13.8 billion years (now) | 2.725 K (CMBR) | Today |
Worked example: temperature, density and ages
- CMB temperature at recombination. The temperature scales as T ∝ 1 + z. With z = 1,100: T = 2.725 × 1,101 = 3,000 K. The peak wavelength at that time: 2.898 × 10−3 ÷ 3,000 = 966 nm (infrared), stretched by 1,101 to 1.06 mm today.
- Peak wavelength today: λmax = 2.898 × 10−3 ÷ 2.725 = 1.06 × 10−3 m. The photons number about 4.1 × 108 per cubic meter (about 411 per cm3), a billion times more than atoms.
- Critical density. H0 = 70 km/s/Mpc = 2.27 × 10−18 s−1. ρc = 3H02 ÷ 8πG = 3 × (2.27 × 10−18)2 ÷ (8π × 6.674 × 10−11) = 1.55 × 10−35 ÷ 1.68 × 10−9 = 9.2 × 10−27 kg/m3, which is about 5.5 hydrogen atoms (1.67 × 10−27 kg) per cubic meter.
- Matter content. Ordinary matter is 5 percent of ρc: 4.6 × 10−28 kg/m3, about 0.3 atoms per cubic meter. Dark matter (27 percent): 2.5 × 10−27 kg/m3. Dark energy (68 percent): 6.3 × 10−27 kg/m3 equivalent.
- Age from the expansion rate. The Hubble time 1/H0 = 14.0 Gyr. The actual age (13.8 Gyr) is close, because the earlier deceleration (by matter) and the later acceleration (by dark energy) almost cancel out in the integral.
- Size of the observable universe. Light from the CMB has traveled for 13.8 billion years, but due to the expansion, the present distance of the source is about 46 billion light-years, giving a radius of the observable universe of about 4.4 × 1026 m.
How did cosmology develop?
Einstein’s general relativity (1915) allowed cosmological models; Alexander Friedmann (1922) and Georges Lemaître (1927) found expanding solutions; Lemaître proposed the “primeval atom” in 1931. Hubble’s observations (1929) supported expansion. George Gamow, Ralph Alpher and Robert Herman predicted the CMBR and nucleosynthesis in 1948. Fred Hoyle, who favored the steady-state model, coined the name “Big Bang” in 1949 on the radio. Penzias and Wilson found the CMBR by accident in 1965 (Nobel Prize 1978), which ended the steady-state theory. Alan Guth proposed inflation in 1981. The 1998 supernova results led to dark energy; the Planck satellite (2013 and 2018) gave the age of 13.8 billion years and the composition. The origin of the universe, the nature of dark matter and dark energy, and the cause of inflation are open questions.
Which mistakes are common?
Mistake 1: Imagining the Big Bang as an explosion in empty space
There was no center and no space “outside”. Space itself expanded everywhere.
Mistake 2: Thinking that dark matter and dark energy are the same thing
Dark matter attracts through gravity and clumps in galaxies. Dark energy is spread uniformly and causes accelerated expansion.
Mistake 3: Believing that the CMBR comes from a particular place in the sky
It comes from all directions. It is the light from the whole early universe.
Mistake 4: Saying that the Big Bang theory explains what happened “before”
The theory describes the evolution from a very hot dense state. The origin of the beginning is unknown, and time before it may not have a meaning in the standard theory.