Attractor solutions for general hessence dark energy

As a candidate for the dark energy, the hessence model has been recently introduced. We discuss the critical points of this model in almost general case, that is for arbitrary hessence potential and almost arbitrary hessence-background matter interaction. It is shown that in all models, there always exist some stable late-time attractors. It is shown that our general results coincide with those solutions obtained earlier for special cases, but some of them are new. These new solutions have two unique characteristics. First the hessence field has finite value in these solutions and second, their stabilities depend on the second derivative of the hessence potential.Comment: 11 pages. Add some explanations about the autonomousity of the equations, and also a conclusion section was added. To appear in Phys. Rev. D (2006

Cosmological coincidence problem in interacting dark energy models

An interacting dark energy model with interaction term $Q= \lambda_m H\rho_m+\lambda_dH\rho_d$ is considered. By studying the model near the transition time, in which the system crosses the w=-1 phantom-divide-line, the conditions needed to overcome the coincidence problem is investigated. The phantom model, as a candidate for dark energy, is considered and for two specific examples, the quadratic and exponential phantom potentials, it is shown that it is possible the system crosses the w=-1 line, meanwhile the coincidence problem is alleviated, the two facts that have root in observations.Comment: 15 pages, LaTeX. Some minor explanations are added. To be published in Phys. Rev.

Generating Functional and Large N-Limit of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM2nlgYM_2's)

Using the path integral method, we calculate the partition function and generating functional (of the field strengths) on the nonlocal generalized 2D Yang - Mills theories ($nlgYM_2$'s), which is nonlocal in auxiliary field [14]. Our calculations is done for general surfaces. We find a general expression for free energy of $W(\phi) = \phi^{2k}$ in $nlgYM_2$ theories at the strong coupling phase (SCP) regime ($A > A_c$) for large groups. In the specific $\phi^4$ model, we show that the theory has a third order phase transition.Comment: tex file, no figure. accepted for publication in Eur. Phys. J. C. (2000