The Big Bang is a Coordinate Singularity for $k=-1$ Inflationary FLRW Spacetimes

Abstract

We show that the big bang is a coordinate singularity for a large class of $k=-1$ inflationary FLRW spacetimes which we have dubbed 'Milne-like.' By introducing a new set of coordinates, the big bang appears as a past boundary of the universe where the metric is no longer degenerate -- a result which has already been investigated in the context of vacuum decay [12]. We generalize their results and approach the problem from a more mathematical perspective. Similar to how investigating the geometrical properties of the $r=2m$ event horizon in Schwarzschild led to a better understanding of black holes, we believe that investigating the geometrical properties of the big bang coordinate singularity for Milne-like spacetimes could lead to a better understanding of cosmology. We show how the mathematics of these spacetimes may help illuminate certain issues associated with dark energy, dark matter, and the universe's missing antimatter.

arXiv comment46 pages, 20 figures, v3 to appear in Foundations of Physics

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• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• Global Hyperbolicity through the Eyes of the Null Distance
• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• A conformal infinity approach to asymptotically ${\text{AdS}}_2\times S^{n-1}$ spacetimes
• Low regularity extensions beyond Cauchy horizons
• Baryogenesis in Minkowski Spacetime
• Tadpole Cosmology: Milne Solution as a Cosmological Constant Hideout
• A lower semicontinuous time separation function for $C^0$ spacetimes