Abstract
We consider a cosmological model with two scalar fields minimally coupled to gravity which have a mixed kinetic term. Hence, Chiral cosmology is included in our analysis. The coupling function and the potential function, which depend on one of the fields, characterize the model we study. We prove the existence of exact solutions that are of special interest for the cosmological evolution. Furthermore, we provide with a methodology that relates the scale factor behaviour to the free functions characterizing the scalar field kinetic term coupling and potential. We derive the necessary conditions that connect these two functions so that the relative cosmological solutions can be admitted. We find that unified dark matter and dark energy solutions are allowed by the theory in various scenarios involving the aforementioned functions.
Highlights
From the detailed analysis of the recent cosmological data [1,2,3] it has been made clear the necessity for the introduction of an exotic fluid term with negative pressure in Einstein’s General Relativity
We considered a two-scalar field cosmological model with a mixed kinetic term
We investigate the existence of some exact solutions for the scale factor which describe different phases in the evolution of the universe
Summary
From the detailed analysis of the recent cosmological data [1,2,3] it has been made clear the necessity for the introduction of an exotic fluid term with negative pressure in Einstein’s General Relativity. The main characteristic of the quintom models is that in general the two scalar fields are minimally coupled and only a few models have been proposed where an interaction term between the two fields is introduced in the potential [37]. The model consists of two unknown functions, the potential which drives the dynamics of the quintessence and the interaction between the fields For this cosmological model we prove the existence of particular solutions of great interest and determine the conditions that they impose in the functions characterizing the theory. We are able to derive – within the type of model we study – which specific relation between the kinetic coupling and the scalar field potential allows for certain interesting cosmological solutions.
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