Equilibrium sets in quintom cosmologies: the past asymptotic dynamics

Abstract

In the previous paper \cite{Lazkoz:2006pa} was investigated the phase space of quintom cosmologies for a class of exponential potentials. This study suggests that the past asymptotic dynamics of such a model can be approximated by the dynamics near a hyperbola of critical points. In this paper we obtain a normal form expansion near a fixed point located on this equilibrium set. We get computationally treatable system up to fourth order. From the structure of the unstable manifold (up to fourth order) we see that that the past asymptotic behavior of this model is given by a massless scalar field cosmology for an open set of orbits (matching the numerical results given in \cite{Lazkoz:2006pa}). We complement the results discussed there by including the analysis at infinity. Although there exists unbounded orbits towards the past, by examining the orbits at infinity, we get that the sources satisfy the evolution rates ${\dot{\varphi }}^2/V\sim \frac{2m^2}{n^2-m^2},\dot{\varphi }/\dot{\phi }\sim -m/n,$ with $H/\dot{\varphi }$ approaching zero.

13 pages, revised version, one error amended. Analysis at infinity added

References in corpus (8)

• Cosmological Evolution of a Quintom Model of Dark Energy
• Dynamical vacuum energy, holographic quintom, and the reconstruction of scalar-field dark energy
• Quintom cosmologies admitting either tracking or phantom attractors
• Quintom cosmologies with arbitrary potentials
• Dark Energy Model with Spinor Matter and Its Quintom Scenario
• Quintom Cosmology with General Potentials
• Reconstructing a String-Inspired Quintom Model of Dark Energy
• The w = -1 crossing of the quintom model with slowly-varying potentials

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• Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models
• Interacting dark matter and q-deformed dark energy non-minimally coupled to gravity