Physical Cosmology

Others took the equations at face value. Alexander Friedmann, a Russian mathematician and meteorologist, showed in 1922 that they allow universes that expand or contract. Georges Lemaître, a Belgian priest and physicist, found the same in 1927 and went further. The observed redshifts of galaxies, measured over the previous decade by Vesto Slipher, were what an expanding universe would produce. Lemaître even estimated the expansion rate.

The observational case was made by Edwin Hubble in 1929. Using the relation between the brightness and pulsation period of Cepheid stars discovered by Henrietta Leavitt, he measured distances to galaxies and found that their recession speeds grow in proportion to distance. The universe is expanding. Run the film backward and everything was once packed together; Lemaître called it the "primeval atom". Einstein visited Hubble in 1931 and accepted the expansion.

For decades expansion did not settle how the universe began. The steady-state theory of Hoyle, Bondi and Gold (1948) proposed that new matter appears continuously as space expands, so the universe has no beginning. Hoyle would coin the name "Big Bang" for the rival idea on BBC radio in 1949. It was widely heard as mockery, though he denied meaning it that way. Meanwhile Ralph Alpher, Robert Herman and George Gamow worked out what a hot beginning implies: the right mix of hydrogen and helium, and a faint radiation left over from the hot early universe, now cooled to a few degrees above absolute zero.

In 1965 Arno Penzias and Robert Wilson found that radiation by accident, as a hiss in a Bell Labs antenna that would not go away. It filled the sky evenly at 2.7 K. The steady state theory could not explain it, and the Big Bang became the standard picture. Satellites since then (COBE, WMAP, Planck) have mapped its tiny ripples, the seeds of all later galaxies, and measured the universe's age as 13.8 billion years.

Hubble's law says that a galaxy at distance $d$ recedes at speed $v = H_0 d$. Today's measurements give $H_0 \approx 70$ km/s per megaparsec, where a megaparsec is $3.09 \times 10^{19}$ km, about 3.3 million light-years.

If every galaxy had always moved at its present speed, they would all have been together a time $d/v = 1/H_0$ ago:

$$\frac{1}{H_0} = \frac{3.09 \times 10^{19} \text{ km}}{70 \text{ km/s}} \approx 4.4 \times 10^{17} \text{ s} \approx 14 \text{ billion years} .$$

The expansion has not been steady, since gravity slowed it early on and dark energy speeds it up now, but the effects nearly cancel. The full calculation gives 13.8 billion years. The oldest stars are about 13 billion years old, consistent with this. Hubble's own value of $H_0$ was about 500, which implied an age of 2 billion years, younger than the Earth. That contradiction made many astronomers wary of the Big Bang for decades.

The cosmic microwave background tells a second story. About 380,000 years after the Big Bang, the universe cooled to around 3,000 K, cool enough for electrons and protons to form neutral hydrogen. Light then travelled freely for the first time. Since then the universe has expanded about 1,100-fold, and the light's wavelengths have stretched by the same factor, cooling it to

$$\frac{3000 \text{ K}}{1100} \approx 2.7 \text{ K} .$$

That is the temperature Penzias and Wilson found, and which satellites have since measured as 2.7255 K. By Wien's law it peaks at a wavelength of about 1 millimetre, in the microwave band, which is why an antenna built for satellite communications picked it up. Two measurements, a rate of expansion and a temperature, describe the same history.

The precision revealed how much is missing. Already in the 1930s Fritz Zwicky noticed that galaxy clusters hold together only if they contain far more mass than can be seen. In the 1970s Vera Rubin's measurements showed the same for individual galaxies, whose outer stars orbit too fast. This dark matter outweighs ordinary matter about five to one.

Then in 1998 two teams, led by Saul Perlmutter and by Brian Schmidt with Adam Riess, found that the expansion is not slowing down under gravity, as expected, but speeding up. Something, now called dark energy, pushes it. Einstein's discarded $\Lambda$ fits the data. By current measurements ordinary matter is about 5% of the universe, dark matter about 27%, and dark energy about 68%.

This is the fog at the edge of the relativity thread. The two biggest ingredients of the universe are unexplained, the two best measurements of its expansion rate disagree, and even its global shape, whether space closes back on itself as a finite 3-manifold, is open.