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The so-called Einstein-Aether theory is General Relativity coupled (at secondderivative order) to a dynamical unit time-like vector field (the aether). Itis a Lorentz-violating theory, and gained much attention in the recent years.In the present work, we study the cosmological evolution of Einstein-Aethermodels with power-law-like potential, by using the method of dynamical system.In the case without matter, there are two attractors which correspond to aninflationary universe in the early epoch, or a de Sitter universe in the latetime. In the case with matter but there is no interaction between dark energyand matter, there are only two de Sitter attractors, and no scaling attractorexists. So, it is difficult to alleviate the cosmological coincidence problem.Therefore, we then allow the interaction between dark energy and matter. Inthis case, several scaling attractors can exist under some complicatedconditions, and hence the cosmological coincidence problem could be alleviated.

Cosmological Evolution of Einstein-Aether Models with Power-law-like Potential