Mathematics and Science

Abstract

The simplest Friedmann models, about which astronomers were still arguing in the late nineteen fifties and sixties are dominated by the equation

$${{{{\dot S}^2} + c{k^2}} \over {{S^2}}} = {A \over {{S^3}}}$$

in which Sis the scale factor of the universe, a function of the time, A is a positive constant and kis a topological factor which can be 0 or ±1. No zero of Sexists for S >S ₀where S ₀ is the present day value of S, and this result is not affected by adding positive terms to the right hand side of (1), as for instance a term B/S ⁴due to relativistically-moving particles, e.g. photons or neutrinos. Thus if the simple Friedmann models were correct, a spaceti me singularity, S → 0, would inevitably occur in a time-reversed form of the models. This was the Big-Bang, which has been well-known to astronomers since Hubble and Humason had discovered the expansion of the universe in about 1930.