Essentials of k-essence - art. no. 103510

We recently introduced the concept of "k-essence" as a dynamical solution f or explaining naturally why the universe has entered an epoch of accelerate d expansion at a late stage of its evolution. The solution avoids fine-tuni ng of parameters and anthropic arguments. Instead, k-essence is based on th e idea of a dynamical attractor solution which causes it to act as a cosmol ogical constant only at the onset of matter domination. Consequently, k-ess ence overtakes the matter density and induces cosmic acceleration at about the present epoch. In this paper, we present the basic theory of k-essence and dynamical attractors based on evolving scalar fields with nonlinear kin etic energy terms in the action. We present guidelines for constructing con crete examples and show that there are two classes of solutions, one in whi ch cosmic acceleration continues forever and one in which the acceleration has finite duration.