Statistics of Thawing K-essence Dark Energy Models

Abstract

K-essence is a minimally-coupled scalar field whose Lagrangian density $\mathcal{L}$ is a function of the field value $\varphi$ and the kinetic energy $X=\frac{1}{2}{\partial }_{\mu }\varphi {\partial }^{\mu }\varphi$. In the thawing scenario, the scalar field is frozen by the large Hubble friction in the early universe, and therefore initial conditions are specified. We construct thawing k-essence models by generating Taylor expansion coefficients of $\mathcal{L}(\varphi ,X)$ from random matrices. From the ensemble of randomly generated thawing k-essence models, we select dark energy candidates by assuming negative pressure and non-growth of sub-horizon inhomogeneities. For each candidate model the dark energy equation of state function is fit to the Chevallier-Polarski-Linder parameterization $w(a)\approx w_0+w_a(1-a)$, where $a$ is the scale factor. The thawing k-essence dark models distribute very non-uniformly in the $(w_0,w_a)$ space. About 90\% models cluster in a narrow band in the proximity of a slow-roll line $w_a\approx -1.42{\left(\frac{{\Omega }_m}{0.3}\right)}^{0.64}(1+w_0)$, where ${\Omega }_m$ is the present matter density fraction. This work is a proof of concept that for a certain class of models very non-uniform theoretical prior on $(w_0,w_a)$ can be obtained to improve the statistics of model selection.

Comments: to appear on PRD