A new view of k-essence

K-essence models, relying on scalar fields with non-canonical kinetic terms, have been proposed as an alternative to quintessence in explaining the observed acceleration of the Universe. We consider the use of field redefinitions to cast k-essence in a more familiar form. While k-essence models cannot in general be rewritten in the form of quintessence models, we show that in certain dynamical regimes an equivalence can be made, which in particular can shed light on the tracking behaviour of k-essence. In several cases, k-essence cannot be observationally distinguished from quintessence using the homogeneous evolution, though there may be small effects on the perturbation spectrum. We make a detailed analysis of two k-essence models from the literature and comment on the nature of the fine tuning arising in the models.Comment: 7 pages RevTeX4 file with four figures incorporate

K-essence and the coincidence problem

K-essence has been proposed as a possible means of explaining the coincidence problem of the Universe beginning to accelerate only at the present epoch. We carry out a comprehensive dynamical systems analysis of the k-essence models given so far in the literature. We numerically study the basin of attraction of the tracker solutions and we highlight the behaviour of the field close to sound speed divergences. We find that, when written in terms of parameters with a simple dynamical interpretation, the basins of attraction represent only a small region of the phase space.Comment: 5 pages RevTeX4 file with two figures incorporated. Minor changes to match PRD accepted versio

Prospects and Problems of Tachyon Matter Cosmology

We consider the evolution of FRW cosmological models and linear perturbations of tachyon matter rolling towards a minimum of its potential. The tachyon coupled to gravity is described by an effective 4d field theory of string theory tachyon. In the model where a tachyon potential $V(T)$ has a quadratic minimum at finite value of the tachyon field $T_0$ and $V(T_0)=0$, the tachyon condensate oscillates around its minimum with a decreasing amplitude. It is shown that its effective equation of state is $p=-\epsilon/3$. However, linear inhomogeneous tachyon fluctuations coupled to the oscillating background condensate are exponentially unstable due to the effect of parametric resonance. In another interesting model, where tachyon potential exponentially approaches zero at infinity of $T$, rolling tachyon condensate in an expanding universe behaves as pressureless fluid. Its linear fluctuations coupled with small metric perturbations evolve similar to these in the pressureless fluid. However, this linear stage changes to a strongly non-linear one very early, so that the usual quasi-linear stage observed at sufficiently large scales in the present Universe may not be realized in the absence of the usual particle-like cold dark matter.Comment: 12 pages, 3 figure

K-essential Phantom Energy: Doomsday around the Corner? Revisited

We generalize some of those results reported by Gonz\'{a}lez-D\'{i}az by further tuning the parameter ($\beta$) which is closely related to the canonical kinetic term in $k$-essence formalism. The scale factor $a(t)$ could be negative and decreasing within a specific range of $\beta$ ($\equiv -1/\omega$, $\omega$ : the equation-of-state parameter) during the initial evolutional period.Comment: 1 Figure, 6 page

New holographic scalar field models of dark energy in non-flat universe

Motivated by the work of Granda and Oliveros [L.N. Granda, A. Oliveros, Phys. Lett. B {\bf 671}, 199 (2009)], we generalize their work to the non-flat case. We study the correspondence between the quintessence, tachyon, K-essence and dilaton scalar field models with the new holographic dark energy model in the non-flat FRW universe. We reconstruct the potentials and the dynamics for these scalar field models, which describe accelerated expansion of the universe. In the limiting case of a flat universe, i.e. $k = 0$, all results given in [L.N. Granda, A. Oliveros, Phys. Lett. B {\bf 671}, 199 (2009)] are obtained.Comment: 11 page

Dark matter to dark energy transition in k-essence cosmologies

We implement the transition from dark matter to dark energy in k-essence cosmologies for a very large set of kinetic functions $F$, in a way alternative to recent proposals which use generalized Chaplygin gas and transient models. Here we require that the pressure admits a power-law expansion around some value of the kinetic energy where the pressure vanishes. In addition, for suitable values of the parameters of the model, the speed of sound of the dark matter will be low. We first present the discussion in fairly general terms, and later consider for illustration two examples.Comment: 5 pages, revte

The generalized second law in irreversible thermodynamics for the interacting dark energy in a non-flat FRW universe enclosed by the apparent horizon

We investigate the validity of the generalized second law in irreversible thermodynamics in a non-flat FRW universe containing the interacting dark energy with cold dark matter. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. We show that for the present time, the generalized second law in nonequilibrium thermodynamics is satisfied for the special range of the energy transfer constants.Comment: 10 page

Interacting polytropic gas model of phantom dark energy in non-flat universe

By introducing the polytropic gas model of interacting dark energy, we obtain the equation of state for the polytropic gas energy density in a non-flat universe. We show that for even polytropic index by choosing $K>Ba^{\frac{3}{n}}$, one can obtain $\omega^{\rm eff}_{\Lambda}<-1$, which corresponds to a universe dominated by phantom dark energy.Comment: 7 page

Infrared cut-off proposal for the Holographic density

We propose an infrared cut-off for the holographic the dark-energy, which besides the square of the Hubble scale also contains the time derivative of the Hubble scale. This avoids the problem of causality which appears using the event horizon area as the cut-off, and solves the coincidence problem.Comment: 9 pages, 2 figures, to appear in Phys. Lett.