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One of the puzzles of the dark energy problem is the (first) cosmologicalcoincidence problem, namely, {\em why does our universe begin the acceleratedexpansion recently? why are we living in an epoch in which the dark energydensity and the dust matter energy density are comparable?} On the other hand,cosmological observations hint that the equation-of-state parameter (EoS) ofdark energy crossed the phantom divide $w_{de}=-1$ in the near past. Many darkenergy models whose EoS can cross the phantom divide have been proposed.However, to our knowledge, these models with crossing the phantom divide onlyprovide the possibility that $w_{de}$ can cross -1. They do not answer anotherquestion, namely, {\em why crossing the phantom divide occurs recently?} Sincein many existing models whose EoS can cross the phantom divide, $w_{de}$undulates around -1 randomly, {\em why are we living in an epoch $w_{de}<-1$?}This can be regarded as the second cosmological coincidence problem. In thiswork, the cosmological evolution of the vector-like dark energy interactingwith background perfect fluid is investigated. We find that the first andsecond cosmological coincidence problems can be alleviated at the same time inthis scenario.Comment: 15 pages, 8 tables, revtex4; v2: references added; v3: published  versio

Interacting vectorlike dark energy, the first and second cosmological coincidence problems