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

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 φ whose dynamics is driven by a (noncanonical) 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 φ. 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 φ is obtained for different values of the diffusion parameter. The obtained temporal behaviour may be expressed as φ(t/t 0 ) = φ 0 + ε 1 (t/t 0 − 1) + ε 2 (t/t 0 − 1) 2 , where t 0 is the time corresponding to present epoch. The coefficients ε 1 and ε 2 have been found and obtained as linear functions of diffusion parameter. 1

Modified scaling in $k$-essence model in interacting dark energy - dark matter scenario

“…The second kind of models, as widely discussed in literature, includes the Quintessence [17,18,19,20,21,22,23,24,25] and k-essence models [26,27,28,29,30,31,32,33]. A sub-class of such models involves consideration of interaction between DE and DM [34,35,36,37,38,39,40,41,42,43] to explain the present-day observed features of cosmic expansion. We have considered such a model in the context of this paper.…”

Time-dependent diffusive interactions between dark matter and dark energy in the context of k-essence cosmology

“…The interaction between DM and DE is assumed to happen through velocity diffusion of particles of DM fluid in the background of field φ. In an earlier work (Bandyopadhyay & Chatterjee 2019a), we studied implications of such a diffusive interaction with constant (time independent) diffusion coefficient. In this work, we revisit an interacting model of DE and DM with a time-dependent diffusion coefficient.…”

“…The basic framework of the model of DM-DE interactions has been discussed in detail in Bandyopadhyay & Chatterjee (2019a); Velten & Calogero (2014). We, first, indulge in a brief recollection of the model with an emphasis on the consideration of the time-dependence of the diffusion coefficient.…”

Realizing interactions between dark matter and dark energy using k-essence cosmology

“…The interaction between DM and DE is assumed to happen through velocity diffusion of particles of dark matter fluid in the background of field φ. In an earlier work [3], we have studied implications of such a diffusive interaction with constant (time independent) diffusion coefficient. In this work we revisit interacting model of DE and DM with a time-dependent diffusion coefficient.…”

“…The basic framework of the model of DM-DE interactions has been discussed in detail in [3,8]. We, first, indulge in a brief recollection of the model with an emphasis on the consideration of the time-dependence of the diffusion coefficient.…”