Abstract
We perform a detailed analysis for the asymptotic behaviour for the multi-scalar field Chiral cosmological scenario. We present the asymptotic behaviour for the one-field, two-fields and three-fields Chiral models. From these results, and deriving conserved quantities, we present a Theorem for the N-fields model for the Chiral model with N-fields. We find that the maximum number of scalar fields which provide interesting physical results at the background level is two-fields, while for N>2 the new stationary points are only of mathematical interest since they do not describe new exact solutions different from those recovered for N=2.
Highlights
The detailed analysis of the recent cosmological observations indicated that our universe has gone through two acceleration phases [1,2,3,4,5,6,7]
The main approaches are based on the introduction of scalar fields in the gravitational field equations [15,16,17,18,19], or are based on the introduction of other geometrodynamical terms which follow from the modification of the Einstein–Hilbert Action [20,21]
In particular we study the asymptotic behaviour of this multi-field model and we attempt to answer the questions of what the maximum number of fields is, and when we get the results of physical interests from
Summary
The detailed analysis of the recent cosmological observations indicated that our universe has gone through two acceleration phases [1,2,3,4,5,6,7]. In [58] the dynamics of a multi-scalar field cosmology model was studied for a model which consists of various quintessence fields with independent scalar field potential. In particular we study the asymptotic behaviour of this multi-field model and we attempt to answer the questions of what the maximum number of fields is, and when we get the results of physical interests from. In the two- and three-scalar field models, the only possible attractors are those of the quintessence theory, which is an interesting result because these multi-field models can be used either to describe the matter era if the model will be considered as a unification of the dark-energy and dark matter model, or by being considered as an inflationary model with two different behaviours in the inflationary era.
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