Chaotic Friedmann-Robertson-Walker cosmology

Abstract

We show that the dynamics of a spatially closed Friedmann -Robertson -Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations to our ability to predict the value of the field at the Big Crunch, from its given value at the Big Bang.PACS 04.20.Cv, 98.80.Bp, 03.20.+i

Chaotic dynamics and two-field inflation

“…In this paper we present prima facie evidence that the dynamics of realistic inflationary cosmological models based on two coupled scalar fields can be chaotic. 1 Chaotic dynamics in models consisting of a single (non-minimally coupled) scalar field in a Robertson-Walker background have been studied by several authors [2,3,4,5]. Moreover, Cornish and Shellard [6] show that the familiar inflationary model of a minimally coupled field with a quadratic potential exhibits chaotic dynamics when spacetime has positive spatial curvature.…”

Periodic orbits of the generalized Friedmann–Robertson–Walker Hamiltonian systems

“…Theorem 1. At every energy level H = h with h ̸ = 0 the generalized FriedmannRobertson-Walker Hamiltonian system (4) has at least one, two or three periodic solutions if one, two or three of the following conditions hold: For the Hamiltonian (1) studied by Calzeta and Hasi [3] we have the following result, which follows directly from Theorem 1.…”

“…Calzeta and Hasi in [3] present analytical and numerical evidence of the existence of chaotic motion for the simplified Friedmann-Robertson-Walker Hamiltonian (1) H = 1 2 (p 2 Y − p 2 X ) + 1 2 (Y 2 − X 2 ) + b 2 X 2 Y 2 , which modelates a universe, filled with a conformally coupled but massive real scalar field. Although this model is too simplified to be considered realistic, its simplicity itself makes it an interesting testing ground for the implications of chaos in cosmology, either classical, semiclassical or quantum, see for more details [3].…”

“…Although this model is too simplified to be considered realistic, its simplicity itself makes it an interesting testing ground for the implications of chaos in cosmology, either classical, semiclassical or quantum, see for more details [3]. Similar models have been used by Hawking [4] and Page [8] to discuss the relationship between the cosmological and thermodynamic arrow of time, in the framework of quantum cosmology.…”

Integrability and Non-Integrability of Planar Hamiltonian Systems of Cosmological Origin

“…Let us consider the flat Friedman-Robertson-Walker system with self-interacting field [1]. After the canonical transformation (p 1 , q 1 ) → (ip 1 , −iq 1 ) the Hamiltonian function has the form…”