Abstract
The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational "near-minimal" scalar field. This coupling model represents a minimal departure from standard theory by decoupling the scalar field's self-interaction term from the derivative of its potential. By assuming a quadratic potential and a self-interaction term that is proportional to the potential, we derive four new exact Bianchi I solutions. We demonstrate that these solutions produce a diverse range of cosmological phenomena, including Big Bang, Big Crunch, and Big Rip singularities, as well as oscillatory ("cyclic") behaviour. For our exact solutions, these singularities occur in infinite proper time and hence are never truly reachable by an observer. To assess the stability of these cosmologies, we perform a numerical stability analysis against spatially inhomogeneous perturbations of the mean curvature. We find that the oscillatory solution is unstable to perturbations of this type, as are solutions in possession of a crushing singularity. Conversely, solutions with a Big Rip singularity (at infinity) are stable to spatially inhomogeneous perturbations of the mean curvature.