The end of the universe

Will the cosmos expand indefinitely, or will its expansion stop one day? What could stop it? It is clear only gravity could do it. The expansion of the universe, which makes galaxies separate, goes against the gravitational attraction, which tries to hold all bodies together.

If we look at Einstein's cosmic equation of general relativity, the question of whether gravity will succeed in stopping the expansion of the universe depends on the relative values and signs of the three terms in the equation. Depending on them, three things can happen:

The standard cosmological model

Map of the Cosmic Background Radiation

In 1927, the Belgian priest and astronomer Georges Lemaître discovered Hubble’s law.

Yeah that’s right. Hubble did not discover the law until 1929. What happened was that Lemaître published it in French in a low-impact journal (Annales de la Société Scientifique de Bruxelles), while Hubble published it two years later in English in the Proceedings of The National Academy of Sciences, received much more publicity and his name got associated with the discovery.

Combined with Einstein’s cosmological equation, Lemaître-Hubble’s law implies that the universe is expanding. In an article published in 1931 in Nature, Lemaître drew the consequence by proposing the Big Bang theory, so called in derision by its opponent Fred Hoyle in 1950. The name caught on.

In 1948, Ralph Alpher, George Gamow and Robert Herman made two surprising predictions, based on the Big Bang theory: the average composition of the mass of the cosmos (three quarters hydrogen and one quarter helium), and the existence of the cosmic background radiation. Both were confirmed during the sixties. From that point, the Big Bang theory became the standard cosmological theory.

Is there a universe?

The Spanish Wikipedia defines the universe thus:

The universe is the totality of space and time, all forms of matter, energy and momentum, plus the laws and physical constants that govern them. However, this term is also used in slightly different contextual senses and refers to concepts such as cosmos, world or nature. Its study, at the highest scales, is the object of cosmology, a discipline based on astronomy and physics, which describes all the aspects of this universe, together with its phenomena.

Before applying to the universe, the Greek word cosmos meant order and beauty. Notice that this sense is maintained in one of its derivatives, the word cosmetic. The Latin word mundus also has the two meanings: as a noun, it means the world, the totality. As an adjective, clean, neat, elegant. Presumably the first sense was copied from Greece, and to translate the world cosmos they adopted the same word that represented in Latin its other meaning. Finally the word nature (physis in Greek) has phenomenal connotations (rather than to the universe, it refers to what happens in it). From this word come physics (the study of nature) and metaphysics (beyond physics).

Pending problems in the standard cosmological model

The standard cosmological model, prevailing since 1998, is called LCDM and is based on the following statements:

• The universe began with a Big Bang, after which there was a phase of accelerated expansion (inflation), which then declined to levels close to the current ones. Ordinary matter appeared later, formed essentially by hydrogen and helium.
• The average curvature of the cosmos is close to zero (flat universe): three-dimensional space is approximately Euclidean.
• The average density of matter in the cosmos is equivalent to about 30% of the critical density (which separates an open, unlimited expanding cosmos from a closed cosmos that would contract again). Since the ordinary density of matter detected so far represents less than 5% of critical density, the remainder (over 25%) must be an unknown form (dark matter). In fact, it would be what is called cold dark matter, which explains the initials CDM in the name of the model. I talked about dark matter in an earlier post.

Einstein’s mistake

When Einstein formulated in 1915 his theory of general relativity, he soon applied it to the entire universe, deriving the following cosmological equation:

It is curious that this equation is identical to the equation that would result from Newton’s theory of gravitation. There is only one difference: constant k represents, in Newton’s case, the total energy of the universe; in Einstein’s case, its curvature.

Each term of this equation contains a universal constant. Besides k, G is the gravitational constant; L is called the cosmological constant, whose interpretation is not clear. Einstein initially thought he could eliminate this term by making L = 0, which simplifies the equation and makes it analytically solvable. Then he discovered that the solution, in that case, was a universe in constant expansion. Since he believed that the universe had to be stationary, he decided to assign the constant a critical value L = L_c, to make it be so.