No-Go Theorem for $k$-Essence Dark Energy

We demonstrate that if $k$-essence can solve the coincidence problem and play the role of dark energy in the Universe, the fluctuations of the field have to propagate superluminally at some stage. We argue that this implies that successful $k$-essence models violate causality. It is not possible to define a time ordered succession of events in a Lorentz invariant way. Therefore, $k$-essence cannot arise as a low energy effective field theory of a causal, consistent high energy theory.

Figure 1

The ratio of $k$-essence to the total energy density ${\Omega }_k$ as function of $1+z$ for the example (16).

Figure 2

The equation of state parameter $w_k$ and sound velocity $c_s^2$ as functions of $1+z$ for the example (16).