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

摘要

We model the standard ΛCDM model of the universe by the spatially flat FLRW line element dsΛCDM2 = ?c2dt2 + 8πGρm,0 Λc22/3 sinh 1 23Λct4/3dσ Euclid2 which we extend for all time t ∈ (?∞,∞). Although there is a cosmological singularity at the big bang t = 0, since the spatial part of the metric collapses to zero, nevertheless, this line element is defined for all time t ∈ (?∞,∞), is C∞ for all t≠0, is C1 differentiable at t = 0, and is non-degenerate and solves Friedmann’s equation for all t≠0. Thus, we can use this extended line element to model the universe from its past-asymptotic initial state dS4? at t = ?∞, through the big bang at t = 0, and onward to its future-asymptotic final state dS4+ at t = ∞. 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 t = ?∞ from an unstable vacuum negative half de Sitter dsdS4?2 initial state and then dies asymptotically at t = ∞ as the stable positive half de Sitter dsdS4+2 final state. Since the de Sitter states are vacuum matter states, our model shows that the universe was created from nothing at t = ?∞ and dies at t = ∞ to nothing.