Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-12-03
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
13 pages, revised version, one error amended. Analysis at infinity added
Scientific paper
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 $\dot\phi^2/V\sim\frac{2m^2}{n^2-m^2}, \dot\phi/\dot\varphi\sim-m/n,$ with $H/\dot\phi$ approaching zero.
Cardenas Rolando
Leon Genly
Morales Jorge Luis
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