Fine-tuned universe facet of physical constant
Examples
Martin Rees formulates the fine-tuning of the universe in terms of the following six dimensionless physical constants.
N, the ratio of the electromagnetic force to the gravitational force between a pair of protons, is approximately 1036. According to Rees, if it were significantly smaller, only a small and short-lived universe could exist.
Epsilon (ε), a measure of the nuclear efficiency of fusion from hydrogen to helium, is 0.007: when four nucleons fuse into helium, 0.007 (0.7%) of their mass is converted to energy. The value of ε is in part determined by the strength of the strong nuclear force. If ε were 0.006, a proton could not bond to a neutron, and only hydrogen could exist, and complex chemistry would be impossible. According to Rees, if it were above 0.008, no hydrogen would exist, as all the hydrogen would have been fused shortly after the Big Bang. Other physicists disagree, calculating that substantial hydrogen remains as long as the strong force coupling constant increases by less than about 50%.
Omega (Ω), commonly known as the density parameter, is the relative importance of gravity and expansion energy in the universe. It is the ratio of the mass density of the universe to the "critical density" and is approximately 1. If gravity were too strong compared with dark energy and the initial metric expansion, the universe would have collapsed before life could have evolved. If gravity were too weak, no stars would have formed.
Lambda (Λ), commonly known as the cosmological constant, describes the ratio of the density of dark energy to the critical energy density of the universe, given certain reasonable assumptions such as that dark energy density is a constant. In terms of Planck units, and as a natural dimensionless value, Λ is on the order of 10−122. This is so small that it has no significant effect on cosmic structures that are smaller than a billion light-years across. A slightly larger value of the cosmological constant would have caused space to expand rapidly enough that stars and other astronomical structures would not be able to form.
Q, the ratio of the gravitational energy required to pull a large galaxy apart to the energy equivalent of its mass, is around 10−5. If it is too small, no stars can form. If it is too large, no stars can survive because the universe is too violent, according to Rees.
D, the number of spatial dimensions in spacetime, is 3. Rees claims that life could not exist if there were 2 or 4 spatial dimensions. Rees argues this does not preclude the existence of ten-dimensional strings.Max Tegmark has argued that if there is more than one time dimension, then physical systems' behavior could not be predicted reliably from knowledge of the relevant partial differential equations. In such a universe, intelligent life capable of manipulating technology could not emerge. Moreover protons and electrons would be unstable and could decay into particles having greater mass than themselves. (This is not a problem if the particles have a sufficiently low temperature.)Top-down cosmology
Stephen Hawking and Thomas Hertog proposed that the universe's initial conditions consisted of a superposition of many possible initial conditions, only a small fraction of which contributed to the conditions we see today. On their theory, it is inevitable that we find our universe's "fine-tuned" physical constants, as the current universe "selects" only those histories that led to the present conditions. In this way, top-down cosmology provides an anthropic explanation for why we find ourselves in a universe that allows matter and life, without invoking the ontic existence of the Multiverse.
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