A simple all-time model for the birth, big bang, and death of the universe

We model the standard [Formula: see text]CDM model of the universe by the spatially flat FLRW line element [Formula: see text] which we extend for all time [Formula: see text]. Although there is a cosmological singularity at the big bang [Formula: see text], since the spatial part of the metric collapses to zero, nevertheless, this line element is defined for all time [Formula: see text], is [Formula: see text] for all [Formula: see text], is [Formula: see text] differentiable at [Formula: see text], and is non-degenerate and solves Friedmann’s equation for all [Formula: see text]. Thus, we can use this extended line element to model the universe from its past-asymptotic initial state [Formula: see text] at [Formula: see text], through the big bang at [Formula: see text], and onward to its future-asymptotic final state [Formula: see text] at [Formula: see text]. Since in this model the universe existed before the big bang, we conclude that (1) the universe was not created de novo at the big bang and (2) cosmological singularities such as black holes or the big bang itself need not be an end to spacetime. Our model shows that the universe was asymptotically created de novo out of nothing at [Formula: see text] from an unstable vacuum negative half de Sitter [Formula: see text] initial state and then dies asymptotically at [Formula: see text] as the stable positive half de Sitter [Formula: see text] final state. Since the de Sitter states are vacuum matter states, our model shows that the universe was created from nothing at [Formula: see text] and dies at [Formula: see text] to nothing.