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3. THE NUMBERS THAT DESCRIBE THE UNIVERSE

Since it appears that the set of numbers required to statistically describe the cosmological model has just seven elements, then these values become important quantities that should be better known, among astronomers and non-astronomers alike. Many people follow the detailed statistics of their favourite sports teams, or can name the capital cities of various countries, or give the sequence of colours of the rainbow, or list the wives of Henry VIII in order, or name the actors who have played their favourite time-travelling alien. Almost everyone learns the list of planets in the Solar System, through the mnemonic about pizzas (that no longer includes pizza!). So why don't most humans know the numbers that describe the Universe that we live in?

Perhaps one of the problems is that the usual six parameters coming from CMB anisotropies are quite esoteric. This becomes apparent as soon as one tries to explain the values in Table I to the general public. However, these six arcane numbers (together with the assumptions that we've already discussed) span the space of all parameters, and hence it's easy to present versions that are simpler (like the age of the Universe, t0, or the density of some component, like ρm) in more familiar units. Let us highlight a few variants of quantities that are useful in describing our Universe, in the hope that some of them may catch on! Further examples along these lines can be found in the paper “Cosmic Mnemonics” [8].

Table III. Variants on the numbers that describe our Universe.

Characteristic scale on the CMB sky, θ ≃ 0.6 (think eclipse!)
Radius of observable Universe ≃ 400 Ym
Age of the Universe t0 ≃ 5 trillion days ≃ 5 × 2200 tPl
Age of the Universe is triple the age of the Earth, t0 ≃ 3 t
H0 t0 is slightly less than 1, and H t will be unity in about 1 billion years
H0 will asymptote to the value 56 km s−1 Mpc−1 in the far future
Cosmological constant, Λ ≃ 10−35 s−2 (“ten square attohertz”)
Critical density, ρcrit, corresponds to 5 proton masses per cubic metre
Density ratios, Ωc / Ωb ≃ 2 ΩΛ / Ωm ≃ 5.3
Density parameter for photons, Ωγ ≃ α2
Variance of density in spheres is unity at about 9 Mpc (no h−1)
Amplitude of position-space density perturbations on Hubble scale, σ ≃ 6 × 10−6
Temperature at last scattering epoch TCMB ≃ 3000 K (think M giant!)
Age at last-scattering epoch, trec ≃ 370 kyr
Age at reionisation, treion ≃ 600 Myr
Number of particles in observable Universe ≃ α−42

With enough effort, it's easy to find numerological coincidences. One should obviously be skeptical about claims of significance for such things though! For example, from the table we see that the number of particles in the observable Universe (mostly photons) is about α−42 (where α is the fine-structure constant), and additionally in the standard model, the Earth forms at a redshift corresponding to z = 0.42. These facts could be used to suggest a link with Douglas Adams' universal answer.

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