Statistics of thawing k-essence dark energy models

k essence is a minimally coupled scalar field whose Lagrangian density L is a function of the field value q and the kinetic energy X = 12 partial differential ,0 partial differential 00. 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 L(0, 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) w0 + wa(1 - a), where a is the scale factor. The thawing k-essence dark models distribute very nonuniformly in the (w0, wa) space. About 90% of models cluster in a narrow band in the proximity of a slow-roll line wa -1.42(SZm0.3)0.64(1 + w0), where SZm 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 (w0, wa) can be obtained to improve the statistics of model selection.