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Increasing evidence suggests that most of the energy density of the universe consists of a dark energy component with negative pressure, a "cosmological constant" that causes the cosmic expansion to accelerate. In this paper, we address the puzzle of why this component comes to dominate the universe only recently rather than at some much earlier epoch. We present a class of theories based on an evolving scalar field where the explanation is based entirely on internal dynamical properties of the solutions. In the theories we consider, the dynamics causes the scalar field to lock automatically into a negative pressure state at the onset of matter-domination such that the present epoch is the earliest possible time, consistent with nucleosynthesis restrictions, when it can start to dominate.Introduction. Observations of large scale structure, searches for Type Ia supernovae, and measurements of the cosmic microwave background anisotropy all suggest that the universe is undergoing cosmic acceleration and is dominated by a dark energy component with negative pressure. 1 The dark energy may consist of a cosmological constant (vacuum density) or quintessence, 2 such as a scalar field with negative pressure. In either case, a key challenge is the "cosmic coincidence" problem: Why is it that the vacuum density or scalar field dominates the universe only recently? Until now, either cosmic initial conditions or model parameters (or both) had to be tuned to explain the low density of the dark energy component.In this paper, we explore a new class of scalar field models with novel dynamical properties that avoid the fine-tuning problem altogether. A feature of these models is that the negative pressure results from the non-linear kinetic energy of the scalar field, which we call, for brevity, k-field or k-essence. (This consideration is inspired by earlier studies of k-inflation, kinetic energy driven inflation. 3-5 ). As we will show, for a broad class of theories, there exist attractor solutions which determine the equation-of-state of k-essence during different epochs depending on the equation-ofstate of the background. Effectively, the scalar field changes its speed of evolution in dynamic response to changes in the background equation-of-state. During the radiation-dominated epoch, k-essence is led to be subdominant and to mimic the equation-of-state of radiation. Hence, the ratio of k-essence to radiation density remains fixed. When the universe enters the dust-

We extend the theory of cosmological perturbations to the case when the "matter" Lagrangian is an arbitrary function of the scalar field and its first derivatives. In particular, this extension provides a unified description of known cases such as the usual scalar field and the hydrodynamical perfect fluid. In addition, it applies to the recently proposed k-inflation, which is driven by non-minimal kinetic terms in the Lagrangian. The spectrum of quantum fluctuations for slow-roll and power law k-inflation is calculated. We find, for instance, that the usual "consistency relation" between the tensor spectral index and the relative amplitude of scalar and tensor perturbations is modified. Thus, at least in principle, k-inflation is phenomenologically distinguishable from standard inflation.Introduction. The quantum theory of cosmological perturbations is one of the most interesting examples of quantum field theory in an external classical field. Indeed, the spectrum of metric perturbations generated during inflation is probably the only prediction of quantum field theory in external fields (besides the Casimir effect) which can be tested "experimentally" in the near future. The quantum theory of linearized cosmological perturbations is well developed in the case of a usual scalar field with the standard kinetic

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We recently introduced the concept of "k-essence" as a dynamical solution for explaining naturally why the universe has entered an epoch of accelerated expansion at a late stage of its evolution. The solution avoids fine-tuning of parameters and anthropic arguments. Instead, k-essence is based on the idea of a dynamical attractor solution which causes it to act as a cosmological constant only at the onset of matterdomination. Consequently, k-essence 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 non-linear kinetic energy terms in the action. We present guidelines for constructing concrete examples and show that there are two classes of solutions, one in which cosmic acceleration continues forever and one in which the acceleration has finite duration.

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