Transient Chaos in Scalar Field Cosmology on a Brane

Abstract

We study cosmological dynamics of a flat Randall-Sundrum brane with a scalar field and a negative "dark radiation" term. It is shown that in some situations the "dark radiation" can mimic spatial curvature and cause a chaotic behavior which is similar to chaotic dynamics in closed Universe with a scalar field.The phenomenon of transient chaos in homogeneous cosmological models had been described by D. Page [1] (he studied a closed isotropic Universe with a massive scalar field) even earlier than this concept was formulated and investigated systematically (see, for example, [2,3]). The key feature of this type of chaos is that the dymamical system (in comparison with the well-known case of strange attractors) has a regular regime as its future attractor while particular trajectories can experience a chaotic behavior before reaching this stable regime.

Stable periodic regime in a scalar field cosmology

“…In a general situation this behavior exists even for quadratic potential if the constant C from the constraint equation (5) is sufficiently large and negative. In nonstandard cosmology this type of dynamics exists also in braneworlds [9] and in theories with quadratic curvature corrections to Einstein gravity [10]. It has been already reported that in these two cases the picture of chaotic dynamics changes significantly in comparison with the case of massive scalar field [7,12].…”

Certain aspects of regularity in scalar field cosmological dynamics

“…In nonstandard cosmology this type of dynamics exists also in braneworlds[19] and in theories with quadratic curvature corrections to Einstein gravity[20].…”