Realising Interactions Between Dark Matter and Dark Energy Using $k$-essence Cosmology

Abstract

In this paper we exploit dynamics of a $k-$essence scalar field to realise interactions between dark components of universe resulting in a evolution consistent with observed features of late time phase of cosmic evolution. Stress energy tensor corresponding to a $k-$essence Lagrangian $L=V(\varphi )F(X)$ (where $X=\frac{1}{2}{g}^{\mu \nu }{\nabla }_{\mu }\varphi {\nabla }_{\nu }\varphi$) is shown to be equivalent to an ideal fluid with two components having same equation of state. Stress energy tensor of one of the components may be generated from a constant potential $k-$essence Lagrangian of form $L_1=V_{0}F(X)$ ($V_0$ constant) and that of other from another Lagrangian of form $L_2=V_1(\varphi )F(X)$ with $V=V_0+V_1(\varphi )$. We have shown that, the unified dynamics of dark matter and dark energy described by a single scalar field $\varphi$ driven by a $k-$essence Lagrangian $L=V(\varphi )F(X)$ may be viewed in terms of diffusive interactions between the two hypothetical fluid components `1' and `2' with stress energy tensors equivalent to that of Lagrangians $L_1$ and $L_2$ respectively. The energy transfer between the fluid components is determined by functions $V(\varphi )$, $F(X)$ and their derivatives. Such a realisation is shown to be consistent with the Supernova Ia data with certain constraints on the temporal behaviour of $k-$essence potential $V(\varphi )$. We have described a methodology to obtain such constraints.

13 pages, 4 figures

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• Dynamical analysis of coupled curvature-matter scenario in viable $f(R)$ dark energy models at de Sitter phase
• Exploring the evolution of structure growth in the universe with field-fluid interactions through dynamical stability analysis
• Observational constraints on generic models of non-minimal curvature-matter coupling
• Modified scaling in $k$-essence model in interacting dark energy - dark matter scenario
• A comprehensive dynamical and phenomenological analysis of structure growth in curvature-modulated coupled quintessence scenario