A lagrangian for the k− essence field is set up with canonical kinetic
terms and incorporating the scaling relation of [1]. There are two degrees of
freedom, {\it viz.},q(t)=lna(t) (a(t) is the scale factor) and the
scalar field ϕ, and an interaction term involving ϕ and q(t).The
Euler-Lagrange equations are solved for q and ϕ. Using these solutions
quantities of cosmological interest are determined. The energy density ρ
has a constant component which we identify as dark energy and a component
behaving as a−3 which we call dark matter. The pressure p is {\it
negative} for time t→∞ and the sound velocity cs2=∂ρ∂p<<1. When dark energy dominates, the deceleration
parameter Q→−1 while in the matter dominated era Q∼21. The
equation of state parameter w=ρp is shown to be consistent with
w=ρp∼−1 for dark energy domination and during the matter
dominated era we have w∼0. Bounds for the parameters of the theory are
estimated from observational data.
Keywords: k-essence models, dark matter, dark energy
PACS No: 98.80.-kComment: 16 pages, latex, paper shortened by 2 pages for journal publicatio