2. The coincidences argument against
An argument against an observationally interesting value
of , from our
distrust of accidental coincidences, has
been in the air for decades, and became very influential in the
early 1980s with the introduction of the inflation scenario for
the very early universe.
If the Einstein-de Sitter model in Eq. (35) were a
good approximation at the present epoch, an observer measuring
the mean mass density and Hubble's constant when the age of the
universe was one tenth the present value, or at ten times the
present age, would reach the same conclusion, that the
Einstein-de Sitter model is a good approximation. That is, we
would flourish at a time that is not special in the course of
evolution of the universe. If on the other hand two or more
of the terms in the expansion rate equation (11) made
substantial contributions to the present value of the expansion
rate, it would mean we are present at a special epoch, because
each term in Eq. (11) varies with the expansion factor
in a different way. To put this in more detail, we imagine that the
physics of the very early universe, when the relativistic
cosmological model became a good approximation, set the values
of the cosmological parameters. The initial values of the
contributions to the expansion rate equation had to have been
very different from each other, and had to have been exceedingly
specially fixed, to make two of the
i0's have
comparable values. This would be a most remarkable and
unlikely-looking coincidence. The
multiple coincidences required for the near vanishing of
and
at a redshift not much
larger than unity
makes an even stronger case against LemaƮtre's coasting
model, by this line of argument.
The earliest published comment we have found on this point
is by Bondi (1960,
p. 166), in the second edition of his book
Cosmology. Bondi notes the "remarkable property" of the
Einstein-de Sitter model: the dimensionless parameter we now call
M is
independent of the time at which it is computed
(since it is unity). The coincidences argument follows and extends
Bondi's comment. It is presented in
McCrea (1971,
p. 151). When Peebles was a postdoc, in the early 1960s, in
R. H. Dicke's gravity research group, the coincidences argument
was discussed, but published much later
(Dicke, 1970,
p. 62;
Dicke and Peebles, 1979).
We do not know its
provenance in Dicke's group, whether from Bondi, McCrea, Dicke,
or someone else. We would not
be surprised to learn others had similar thoughts.
The coincidences argument is sensible but not a proof, of course.
The discovery of the 3 K thermal cosmic microwave background radiation
gave us a term in the expansion rate equation that is down from the
dominant one by four orders of magnitude, not such a large factor by
astronomical standards. This might be
counted as a first step away from the argument. The evidence from
the dynamics of galaxies that
M0 is
less than unity is another step
(Peebles, 1984,
p. 442; 1986). And yet another is the development of the evidence that the
and dark
matter terms differ by only a factor of three
(Eq. [2]).
This last is the most curious, but the community has
come to accept it, for the most part. The precedent makes
LemaƮtre's coasting model more socially acceptable.
A socially acceptable value of
cannot be such as to
make life impossible, of course.
(17)
But perhaps the most productive interpretation of the coincidences
argument is that it demands a search for a more fundamental
underlying model. This is discussed further in
Sec. III.E and
the Appendix.
17 If
were negative
and the magnitude too large there
would not be enough time for the emergence of life like us. If
were positive and
too large the universe would expand too rapidly to allow galaxy
formation. Our existence, which requires something resembling the
Milky Way galaxy to contain and recycle heavy elements, thus
provides an upper bound on the value of
.
Such anthropic considerations are discussed by
Weinberg (1987,
2001),
Vilenkin (2001),
and references therein.
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