Diffusive dark matter and dark energy scenario and $k-$essence in the context of Supernova Ia observations

TL;DR

This paper proposes a unified model of interacting dark matter and dark energy using a $k$-essence scalar field, analyzing Supernova Ia data to constrain the diffusion parameter and study the scalar field's evolution.

Contribution

It introduces a novel interacting dark matter-dark energy model with a $k$-essence scalar field and derives bounds on the diffusion parameter from observational data.

Findings

Bounds on the diffusion coefficient from Supernova Ia data

Temporal behavior of the $k$-essence scalar field expressed as a quadratic function of time

Linear dependence of scalar field coefficients on the diffusion parameter

Abstract

We consider a unified model of interacting dark matter and dark energy to account for coincidence of present day dark energy and dark matter densities. We assume dark energy to be represented by a homogeneous scalar field $\phi$ whose dynamics is driven by a (non-canonical) $k$-essence Lagrangian with constant potential and the particles of dark matter fluid undergoing velocity diffusion in background medium of the $k-$essence scalar field $\phi$. This results in a transfer of energy from the fluid of dark matter to that of dark energy. This effect shows up as a source term in the continuity equation for dark matter and dark energy fluids. The source term involves a diffusion coefficient which is a measure of average energy transferred per unit time due to diffusion. We use time evolutions of the scale factor of background FRW spacetime, energy density and pressure of the dark fluid obtained from analysis of Supernova Ia data to obtain bounds on the diffusion parameter. For a constant potential in the $k$-essence Lagrangian, the temporal behaviour of a homogeneous $k$-essence field $\phi$ is obtained for different values of the diffusion parameter. The obtained temporal behaviour may be expressed as $\phi(t/t_0) = \phi_0 + \varepsilon_1 (t/t_0 - 1) + \varepsilon_2 (t/t_0 -1)^2$, where $t_0$ is the time corresponding to present epoch. The coefficients $\varepsilon_1$ and $\varepsilon_2$ have been found and obtained as linear functions of diffusion parameter.