On 3+1 Dimensional Friedman-Robertson-Walker Universes with Matter

TL;DR

This paper investigates the behavior of matter fields in 3+1 dimensional Friedmann-Robertson-Walker universes, revealing nonlinear dynamics and finite-time blowup phenomena with implications for quantum cosmology.

Contribution

It provides new analytical solutions for scalar fields coupled to gravity in cosmological models, highlighting nonlinear effects and potential links to quantum cosmology.

Findings

Regular solutions in the massless case

Asymptotic solutions in the massive case

Finite-time blowup phenomena

Abstract

We examine the dynamical behavior of matter coupled to gravity in the context of a linear Klein-Gordon equation coupled to a Friedman-Robertson-Walker metric. The resulting ordinary differential equations can be decoupled, the effect of gravity being traced in rendering the equation for the scalar field nonlinear. We obtain regular (in the massless case) and asymptotic (in the massive case) solutions for the resulting matter field and discuss their ensuing finite time blowup in the light of earlier findings. Finally, some potentially interesting connections of these blowups with features of focusing in the theory of nonlinear partial differential equations are outlined, suggesting the potential relevance of a nonlinear theory of quantum cosmology.