The instability of critical and underdense Friedmann spacetimes at the Big Bang as an alternative to dark energy

Abstract

Abstract – We characterize the local instability of pressureless Friedmann spacetimes to radial perturbation at the Big Bang. The analysis is based on a formulation of the Einstein–Euler equations in self-similar variables (Formula presented), with (Formula presented), conceived to realize the critical ((Formula presented)) Friedmann spacetime as a stationary solution whose character as an unstable saddle rest point (Formula presented) is determined via an expansion of smooth solutions in even powers of (Formula presented). The eigenvalues of (Formula presented) imply the (Formula presented) Friedmann spacetimes are unstable solutions within the unstable manifold of (Formula presented). We prove that all solutions smooth at the centre of symmetry agree with a Friedmann spacetime at leading order in (Formula presented), and with an eye toward cosmology, we focus on (Formula presented), the set of solutions which agree with a (Formula presented) Friedmann spacetime at leading order, providing the maximal family into which generic underdense radial perturbations of the unstable critical Friedmann spacetime will evolve. We prove solutions in (Formula presented) generically accelerate away from Friedmann spacetimes at intermediate times but decay back to the same leading-order Friedmann spacetime asymptotically as (Formula presented). Thus instabilities inherent in the Einstein–Euler equations provide a natural mechanism for an accelerated expansion without recourse to a cosmological constant or dark energy.