Dirac Large Numbers Hypothesis

The Dirac large numbers hypothesis uses the ratio of the size of the visible universe to the radius of quantum particle to predict the age of the universe. 

The coincidence of various ratios being close in order of magnitude may ultimately prove meaningless or the indication of a deeper connection between concepts in a future theory of everything. Nevertheless, attempts to use such ideas have been criticized as numerology.

The Dirac large numbers hypothesis (LNH) is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch. According to Dirac's hypothesis, the apparent equivalence of these ratios might not be a mere coincidence but instead could imply a cosmology with these unusual features:

• The strength of gravity, as represented by the gravitational constant, is inversely proportional to the age of the universe:
• The mass of the universe is proportional to the square of the universe's age: .

Neither of these two features has gained wide acceptance in mainstream physics and, though some proponents of non-standard cosmologies refer to Dirac's cosmology as a foundational basis for their own ideas and studies, some physicists dismiss the large numbers in LNH as mere coincidences.

A coincidence, however, may be defined optimally as 'an event that provides support for an alternative to a currently favoured causal theory, but not necessarily enough support to accept that alternative in light of its low prior probability.' 

Research into LNH, or the large number of coincidences that underpin it, appears to have gained new impetus from failures in standard cosmology to account for anomalies such as the recent discovery that the universe might be expanding at an accelerated rate.

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Early General Relativity Based Cosmologies

See also: De Sitter universe and Static universe

Before the present general relativistic cosmological model was developed, Albert Einstein proposed a way to dynamically stabilize a cosmological scenario that would necessarily collapse in on itself due to the gravitational attraction of the matter constituents in the universe. Such a universe would need a source of "anti-gravity" to balance out the mutual attraction, a scalar term in Einstein's equations that would come to be known as the cosmological constant. 

Einstein's first attempt at modeling relied on a cosmological constant that was finely tuned to exactly balance out matter curvature and provide a framework for an infinite and unchanging spacetime metric in which the objects of the universe were embedded. This happens to be the same as a special case of the current cosmological model where the cosmic scale factor is unchanging and the density seen in the Friedmann equations is equally divided between the cosmological constant and matter.

Willem de Sitter would later generalize Einstein's scalar potential model to a universe model that would expand exponentially. As the early development of the Big Bang theory began, De Sitter would be falsely credited for inventing the expanding universe metric because of this. In reality, it was the work of Alexander Friedman and Georges Lemaître who established the metric that would come to be the most accepted for cosmology. Nevertheless, De Sitter's model appears in two places today: in the discussion of cosmic inflation and in the discussion of dark energy dominated universes.

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Alternative metric cosmologies

The Friedmann–Lemaître–Robertson–Walker metric that is necessary for the Big Bang and Steady State models emerged in the decade after the development of Einstein's general relativity and was accepted as a model for the universe after Edwin Hubble's discovery of his eponymous law. It was not clear early on how to find a "universe solution" to Einstein's equations that allowed for a universe that was infinite, unending, and immutable (scientists of the time assumed for philosophical reasons the universe should have such a character).

Even after the development of expanding universe theories, people would engage in this exercise from time to time when looking for a replacement for general relativity. Any alternative theory of gravity would imply immediately an alternative cosmological theory since current modeling is dependent on general relativity as a framework assumption. What is included are a number of models based on alternative gravitational scenarios as well as early attempts to derive cosmological solutions from relativity.