Statistics of Thawing K-essence Dark Energy Models

TL;DR

This paper explores the statistical properties of thawing k-essence dark energy models by generating random Lagrangians, fitting their equations of state, and analyzing their distribution in parameter space to inform model selection.

Contribution

The study introduces a novel method of generating thawing k-essence models using random matrices and analyzes their distribution in the $(w_0, w_a)$ parameter space, revealing non-uniform priors.

Findings

90% of models cluster near a specific slow-roll line

Models distribute non-uniformly in the $(w_0, w_a)$ space

Provides a new approach to priors for dark energy model selection

Abstract

K-essence is a minimally-coupled scalar field whose Lagrangian density $\mathcal{L}$ is a function of the field value $\phi$ and the kinetic energy $X=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi$. 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 $\mathcal{L}(\phi, X)$ 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.