A classical non-quantum all-time time-symmetrical zero-energy single-bounce model for the creation, big bang, and death of the universe

Abstract

In this paper, we show how the [Formula: see text]CDM (Lambda Cold Dark Matter) Standard Model for cosmology can be extrapolated backwards through the big bang into the infinite past to yield an all-time model of the universe with scale factor given by [Formula: see text] defined and continuous for all [Formula: see text] and smooth ([Formula: see text] and satisfying Friedmann’s equation for all [Formula: see text]. At the big bang [Formula: see text], there is a nondifferentiable cusp singularity and our model shows some details of the behavior of the universe at this singularity. Our model is a zero-energy single-bounce model and an examination of the [Formula: see text]-plot of the [Formula: see text] level curve gives critical information about the initial and final states of the universe, about the evolution of the universe, and about the behavior of the universe at the big bang. Our results show that much can be said classically about the birth, big bang and death of the universe before one needs to reach for quantum gravitational effects.