Dirac large numbers hypothesis

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 similarity 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: ${\displaystyle G\propto 1/t\,}$
• The mass of the universe is proportional to the square of the universe's age: ${\displaystyle M\propto t^{2}}$.
• Physical constants are actually not constant. Their values depend on the age of the Universe.

Stated in another way, the hypothesis states that all very large dimensionless quantities occurring in fundamental physics should be simply related to a single very large number, which Dirac chose to be the age of the universe.^[1]