Indeterminacy in classical cosmology with dark matter

TL;DR

This paper explores a unique indeterminacy in classical cosmology with dark matter, where the initial conditions of the universe's evolution are not uniquely determined, but can be resolved through relational dynamics.

Contribution

It introduces a new case of indeterminacy in the evolution of spacetime in homogeneous, isotropic cosmologies with dark energy fluids, extending previous studies.

Findings

Indeterminacy occurs at the onset of the Big Bang.

Relational dynamics can resolve the indeterminacy.

The model generalizes previous indeterminacy cases.

Abstract

We describe a case of indeterminacy in general relativity for homogeneous and isotropic cosmologies for a class of dark energy fluids. The cosmologies are parametrized by an equation of state variable, with one instance giving the same solution as Norton's mechanical dome. Our example goes beyond previously studied cases in that indeterminacy lies in the evolution of spacetime itself: the onset of the Big Bang is indeterminate. We show further that the indeterminacy is resolved if the dynamics is viewed relationally.