Are the multiverse theories scientific?

Virgo galactic cumulus

In previous posts I have said that the theories of the multiverse (there are several, some of them contradictory to the others) are not scientific, because it’s not possible to prove them false, according to Karl Popper’s criterion: a theory is not scientific unless it can be proved false with an experiment.

A recent article by Man Ho Chan reviews and refutes various attempts to claim that multiverse theories are indeed scientific. Here I am going to speak about those that try to prove that the multiverse theories should be considered scientific without asking big changes to the current criteria. Carroll 2018 uses three main arguments to justify this:

The mystery of the cosmological constant

Alexander Friedmann
(Александр Фридман)

This post completes a previous post with a similar title:

The problem of the cosmological constant.

First of all, we should define three different concepts that could be closely related:

1. Vacuum energy: due to the constant appearance of pairs of particles and antiparticles that immediately mutually disintegrate, so they are undetectable through direct experimentation. Their appearance is a consequence of the uncertainty principle: ΔE×Δt<ħ/2, which implies that a particle with energy ΔE can appear spontaneously during a time Δt<ħ/(2ΔE), which is smaller for larger ΔE. Thus, a virtual electron would last less than 4×10^-21 seconds. A proton, whose mass is 1837 times greater, would last 1837 times less. By applying quantum field theory to all the known particles, the energy of the vacuum can be estimated.
2. The cosmological constant: introduced by Einstein in his cosmological equation, which in the format devised by Alexander Friedman is expressed as follows: The symbol Λ is the cosmological constant. Einstein proposed a negative value, to compensate for a cosmic expansion, in which he initially did not believe. Today it is thought to be positive, which would explain the accelerated expansion of the universe discovered in 1998.

3. Dark energy: an unknown agent that would cause the accelerated expansion of the universe.

The problem of the cosmological constant

Albert Einstein

The value of the cosmological constant Λ in Einstein's equation has gone through many vicissitudes and alternatives:

Is there energy in the cosmos?

Georges Lemaître

During the 1950s two cosmological theories entered in competition: the Big Bang, proposed by Georges Lemaître, and the steady state, proposed by Hermann Bondi and Thomas Gold. Although the second had to renounce the principle of the conservation of energy, the most sacred of physics, atheist cosmologists preferred it to the Big Bang, as it seemed to them that this theory required to accept God's creation. In the words of the English astronomer Raymond Littleton, in his popularization book The Modern Universe (1956):

A theory such as this [the Big Bang] that puts back creation to a singular instant in the remote past... to some minds it is an objection that it would imply the removal of the question of the origin of the material of the universe from the realm of science... This consideration does not of course mean that the explosion theory is necessarily wrong, but it puts the act of creation, as we might name it, beyond the reach of science.

In other words: Raymond Littleton objects to the Big Bang theory because it could force us to recognize the existence of a creative God. It cannot be said more clearly.

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.

Dark energy again

Albert Einstein

In a previous article I mentioned that Einstein introduced a third term in the right side of his cosmological equation, to force this equation to have as solution a stationary cosmos, that would not expand or contract. The attempt was unsuccessful, for such a cosmos would have been in unstable equilibrium, and the smallest variation would have pushed it to either expanding or contracting. The term in question depends on a constant (L, the cosmological constant), which we don’t really know what it is.

Einstein's cosmological equation

For most of the twentieth century, it was assumed that the value of the cosmological constant must be zero. In other words, the third term of the Einstein equation would not exist, wouldn’t be necessary. However, in 1998 it was discovered that the universe seems to be expanding rapidly. At least, this seems to be indicated by the study of supernovas in very distant galaxies, about one billion light-years away from us. To explain this discovery, the cosmological constant term was resurrected, but giving it a sign opposite to that proposed by Einstein, so that rather than the expansion being counteracted, it would be accelerated. This proposal has become the standard cosmological model, in which the first term of the equation, which represents the effect of the mass, currently counts as 31%, while the third, that of the cosmological constant, counts as 69%. In this model, the second is assumed to be zero. I leave apart the question that the mass term does not match, so it has been necessary to assume that there is also a dark matter, that we don’t know what it is.

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.