Attractors and initial-condition sensitivity in Horndeski cosmologies

Abstract

We study whether nearby homogeneous cosmological histories approach or move away from the Genesis and contracting solutions. We also determine how an uncertainty in the scalar velocity at a later stage affects the inferred initial velocity. In the Genesis models, including the gravitational dynamics can substantially change this relation. We find that convergence of homogeneous solutions can occur even around backgrounds with unstable perturbations, and therefore attraction of the background is not sufficient to establish that a cosmological solution is physically viable. In the contracting model, one power-law solution attracts nearby trajectories, whereas another repels them. The strength of these effects depends on how the cosmological state is parametrized. Their evolution through the subsequent bounce is not considered here.