Friedmann’s equation and the creation of the universe

Abstract

In this paper, we present mathematical evidence that the beginning of the universe did not occur at the big bang at [Formula: see text] with the universe in a state of infinite density, but occurred at [Formula: see text] with the universe in a state of infinite dilution. We show the essential importance played by the native quadratic structure of a generic Friedmann’s equation [Formula: see text] in the time derivative [Formula: see text] in arriving at this conclusion and show how this quadratic structure together with the accompanying time-reversal symmetry of Friedmann’s equation has profound physical consequences in building Friedmann models of the universe, one of which is that classical cosmological models can be extrapolated backward through the big bang into the infinite past. We conclude that viable cosmological models based on the native quadratic form of Friedmann’s equation, and thus on Einstein’s equations, show that global spatial singularities need not signal an end to spacetime. Moreover, classical big bang cosmological models based on Friedmann’s equation, without the need for quantum gravity, when globalized to all-time solutions, show that the universe did not begin at the big bang. Thus encoded in Friedmann’s equation is previously undiscovered information about how the universe began and we show that this information can only be extracted when Friedmann’s equation is taken in its native quadratic form as opposed to the usual approach of considering only the positive square root form of Friedmann’s equation.