Interacting Induced Dark Energy Model
  Following the idea of the induced matter theory, for a non-vacuum
five-dimensional version of general relativity, we propose a model in which the
induced terms emerging from the extra dimension in our four-dimensional
space-time, supposed to be as dark energy. Then we investigate the FLRW type
cosmological equations and illustrate that when the scale factor of the fifth
dimension has no dynamics, in early time the universe expands with deceleration
and then in late time, expands with acceleration. In this case, the state
parameter of the effective dark energy has a range of $-1<\bar{w}_{_{X}}<0$ and
it has the value $-1/2$ for present time. The results for current acceleration
impose that $\Omega_{_{X\circ}}>2\Omega_{_{M\circ}}$ which is in agreement with
the measurements. We show that the effective energy density of dark energy have
been having the same order of magnitude of the effective energy density of
matter from the early time in the decelerating epoch of the universe expansion
until now. The model avoids the cosmological coincidence problem.
