Purely kinetic k-essence as unified dark matter

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We examine k-essence models in which the Lagrangian p is a function only of the derivatives of a scalar field phi and does not depend explicity on phi. The evolution of phi for an arbitrary functional form for p can be given in terms of an exact analytic solution. For quite general conditions on the functional form of p, such models can evolve to a state characterized by a density scaling with the scale factor as rho = rho₀ + rho₁(a/a₀)⁻³, but with a sound speed cₛ² << 1 at all times. Such models can serve as a unified model for dark matter and dark energy, while avoiding the problems of the generalized Chaplygin gas models, which are due to a non-negligible sound speed in these models. A dark energy component with cₛ << 1 serves to suppress cosmic microwave background fluctuations on large angular scales.