Scalar field cosmology in phase space

Abstract

Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time quintessence eras. Focussing on the spatially flat case, we examine the geometrical structure of the phase space, locate the equilibrium points of the system (de Sitter spaces with a constant scalar field), study their stability through both a third-order perturbation analysis and Lyapunov functions, and discuss the late-time asymptotics. As we do not specify the scalar field's origin or its potential, the results are independent of the high-energy model.

24 pages, 3 figures, to appear in General Relativity and Gravitation

References in corpus (4)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• The phase space view of f(R) gravity
• The Evolution of Universe with th B-I Type Phantom Scalar Field
• Non-chaotic dynamics in general-relativistic and scalar-tensor cosmology

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• New perturbative method for analytical solutions in single-field models of inflation
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• On the quantum origin of inflation in the geometric inflation model
• Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications
• Cosmological singularities in $f(T,\varphi )$ gravity
• Inflationary equilibrium configurations of scalar-tensor theories of gravity
• Cosmological singularities in non-canonical models of dark energy
• A dynamical systems perspective on the thermodynamics of late-time cosmology
• Non-singular non-flat universes
• Dynamical-System analysis of single-axion monodromy inflation with periodically-modulated potentials
• Revisiting dynamics of interacting quintessence