Purely kinetic k-essence as unified dark matter

TL;DR

The paper addresses whether a single scalar field with a purely kinetic k-essence Lagrangian can act as both dark matter and dark energy. It shows that for $p = F(X)$ with constant potential, the dynamics admit an exact analytic solution $X F_X^2 = k a^{-6}$, enabling a unified description. Near an extremum $X_0$ where $F_X(X_0)=0$, the solution yields a DM-like component with $\rho \propto a^{-3}$ plus a cosmological-constant-like term, while the sound speed remains $c_s^2 \ll 1$, preserving clustering. While advantageous over the generalized Chaplygin gas in avoiding late-time instabilities and damping of CMB at large scales, the model requires fine-tuning of parameters and does not solve the coincidence problem, and its nonlinear clustering behavior requires further study.

Abstract

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 = rho_0 + rho_1(a/a_0)^{-3}, but with a sound speed c_s^2 << 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 << 1 serves to suppress cosmic microwave background fluctuations on large angular scales.