Abstract
The present work deals with dynamical system analysis of a quintom model of dark energy. By suitable transformation of variables the Einstein field equations are converted to an autonomous system. The critical points are determined and stability of hyperbolic critical points are determined by Hartman–Grobman theorem. To analyze non-hyperbolic critical points different tools (notably center manifold theory) are used. Possible bifurcation scenarios have also been explained.
Highlights
An important problem in present cosmology is to comprehend the role of dark energy (DE) which discovered at the turn of last century when two independent observational studies [1,2] from Type Ia Supernovae (SNIa) [3,4] revealed that the universe is going through cosmic acceleration at a fast pace
The coupled potential of the quintom model is chosen as a linear combination of the power-law of the two scalar fields and an exponential product form of the scalar fields
For the linear combination of the power law form of the potential several cases have been discussed for different choices of the powers
Summary
An important problem in present cosmology is to comprehend the role of dark energy (DE) which discovered at the turn of last century when two independent observational studies [1,2] from Type Ia Supernovae (SNIa) [3,4] revealed that the universe is going through cosmic acceleration at a fast pace. Some data analyses suggest the cosmological constant boundary (or phantom divide) is crossed [12,13,14,15,16,17], due to the dynamical behavior of the dark energy. Some of the recent observational data show a significant accordance with a dynamical EoS for the dark energy component corresponding to quintom models. In these models, the dark energy equation of state parameter presenting an evolution from a phantom behavior ωp < −1 around present epoch, towards a quintessence behavior ωQ > −1 in the near past [27,28,29,30].
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