Statistics of thawing $k$-essence dark energy models

$k$ 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 nongrowth of subhorizon inhomogeneities. For each candidate model the dark energy equation of state function is fit to the Chevallier-Polarski-Linder parametrization $w(a)\approx w_0+w_a(1-a)$, where $a$ is the scale factor. The thawing $k$-essence dark models distribute very nonuniformly in the $(w_0,w_a)$ space. About 90% of models cluster in a narrow band in the proximity of a slow-roll line $w_a\approx -1.42{(\frac{{\mathrm{\Omega }}_m}{0.3})}^{0.64}(1+w_0)$, where ${\mathrm{\Omega }}_m$ is the present matter density fraction. This work is a proof of concept that for a certain class of models very nonuniform theoretical prior on $(w_0,w_a)$ can be obtained to improve the statistics of model selection.

Figure 1

EOS of randomly sampled thawing $k$-essence dark energy candidates. Each panel contains 100 random samples.

Figure 2

CPL fittings of randomly sampled thawing $k$-essence models. Each panel contains 1000 random samples. The orange line in each panel is the slow-roll approximation given by Eq. (18).

Figure 3

CPL fittings of randomly sampled thawing $k$-essence models with $|1+w|<0.2$, for ${\mathrm{\Omega }}_m=0.25$ (200 skyblue dots) and ${\mathrm{\Omega }}_m=0.4$ (200 orange dots), respectively. The solid lines are the slow-roll approximation given by Eq. (18).

Figure 4

Comparison between Eq. (21) and its numeric approximation Eq. (18).

Figure 5

The marginalized 68.3%, 95.4%, 99.7% confidence-level contours of $w_0$, $w_a$, $V_{00}$, and a few selected $V_{ij}$ coefficients.