Testing a dissipative kinetic k-essence model

Abstract

In this work, we present a study of a purely kinetic k-essence model, characterized basically by a parameter α in presence of a bulk dissipative term, whose relationship between viscous pressure and energy density ρ of the background follows a polytropic type law, ∝ ρ λ+1/2 , where λ, in principle, is a parameter without restrictions. Analytical solutions for the energy density of the k-essence field are found in two specific cases: λ = 1/2 and λ = (1 − α)/2α, and then we show that these solutions possess the same functional form as the non-viscous counterpart. Finally, both approaches are contrasted with observational data from type Ia supernova, and the most recent Hubble parameter measurements, and therefore, the best values for the parameters of the theory are found.

General Bulk-Viscous Solutions and Estimates of Bulk Viscosity in the Cosmic Fluid

“…As Ref. [34] formulates it, the most common dependencies ζ ∝ ρ and ∝ √ ρ are chosen because they lead to well known analytic solutions. Any attempt at extrapolating the theory into the future will involve knowledge about the functional form of ζ.…”

“…where λ ≥ 0, and ζ 0 is the present viscosity. The above ansatz, for some power of λ, has often been used in the literature, both for the early universe [30][31][32][33] and for the later universe [4,5,8,[34][35][36]. The two most actual values for λ are λ = 1 2 whereby ζ ∝ θ ∝ √ ρ, and λ = 1 whereby ζ ∝ θ 2 ∝ ρ.…”

Remarks on Cosmological Bulk Viscosity in Different Epochs

“…By now, the literature is rich with contributions on the topic of viscous cosmology. The contributions include investigations of the early universe [13][14][15][16], the late universe [17][18][19], the phantom divide [20][21][22][23][24][25], models for the dark sector [26][27][28][29], and others [30][31][32][33][34][35][36][37][38][39].…”

Remarks on cosmological bulk viscosity in different epochs

“…the phantom divide [20][21][22][23][24][25], models for the dark sector [26][27][28][29], and others [30][31][32][33][34][35][36][37][38][39].…”