Purely Kinetic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi></mml:math>Essence as Unified Dark Matter

Abstract

We examine $k$-essence models in which the Lagrangian $p$ is a function only of the derivatives of a scalar field $\ensuremath{\varphi}$ and does not depend explicitly on $\ensuremath{\varphi}$. The evolution of $\ensuremath{\varphi}$ 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 $\ensuremath{\rho}$ scaling with the scale factor $a$ as $\ensuremath{\rho}={\ensuremath{\rho}}_{0}+{\ensuremath{\rho}}_{1}(a/{a}_{0}{)}^{\ensuremath{-}3}$, but with a sound speed ${c}_{s}^{2}\ensuremath{\ll}1$ 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 ${c}_{s}\ensuremath{\ll}1$ serves to suppress cosmic microwave background fluctuations on large-angular scales.