The trunk of the cosmic elephant

The Standard Model of Cosmology (SMC) is also known by the acronym in English (and Greek!) ΛCDM. The eleventh Greek letter Λ (capital λ — lambda) represents the dark energy component, which is attributed, almost unanimously, to a cosmological constant (a specific version of the so-called “vacuum energy”). The acronym CDM means “Cold Dark Matter”. It refers to non-baryonic matter (exotic matter), which is “cold” for being non-relativistic, i.e., with velocities much smaller than the speed of light in vacuum (in contrast, for example, with the neutrino, which is relativistic non-baryonic matter; but beware, contrary to CDM, neutrinos are not dark, because they were already observed long time ago, in the end of the 1950s).

The chapter 23 of Review of Particle Physics 2012 is entitled The Cosmological Parameters and was written by the cosmologists O. Lahav (University College London) and A.R. Liddle (University of Edinburgh). The authors show, in section 23.3, a review of the cosmological observations that the ΛCDM model must explain (distant supernovae, microwave background radiation, clustering of galaxies, etc.). Table 23.1 lists the six adjustable parameters, also called “free parameters”, of ΛCDM. In addition to the parameters related to the primordial density fluctuations and to the background radiation, there are the densities of baryonic matter and of dark matter. In fact, the number of free parameters should be greater because the following assumptions are made: the initial (primordial) spectrum of density fluctuations is a power law, the spatial geometry is flat, and the dark energy is given by a cosmological constant. Without these assumptions, the number of free parameters would be much greater than six.

What is more appalling, however, is that all free parameters of the SMC represent properties of physical entities over whose existences nothing is known from the observational point of view. The most obvious situations are those of non-baryonic dark matter and dark energy. Also, all the other adjustable parameters of the ΛCDM theory represent physical characteristics of “genuine working hypotheses”, if not to say, of “plain speculations”.

Now, do six free parameters represent a reasonable number for a physical theory to be considered respectable? No, they do not, according to the opinion of a well-known Nobel laureate in physics. Otherwise, let us see.

The British theoretical physicist, living in the United States, Freeman Dyson wrote a short note entitled “TURNING POINTS – A meeting with Enrico Fermi”, in which he describes an encounter he had with the renowned Italian, settled in the United States, theoretical and experimental physicist Enrico Fermi (1901-1954). Freeman Dyson showed Fermi the results of his theory for the meson-proton scattering, based on quantum electrodynamics. The intention was to show the good fitting of the theory with Fermi's experimental data. Fermi did not like Dyson's approach to the problem, not being impressed with the agreement between theory and experiment. He then asked how many free parameters he had in his theory. Freeman Dyson answered: “— Four.”

In order to justify the bad impression he had, Fermi mentioned another great scientist and his friend, the Hungarian, also living in the United States, John von Neumann (1903-1957). He, when referring to theoretical models, used to say that

“(...) with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”