Renyi entropy and the holographic dark energy in flat space time
  Based on Renyi entropy, we study the entropy corrected version of the
holographic dark energy (HDE) model in apparent horizon of spatially flat FLRW
universe. Applying the generalized entropy leads to the modified version of the
Friedmann evolution equations which besides pressure-less matter and HDE, there
is an extra term that is purely geometric. This extra term are assumed as
another part of dark energy. We assume the universe is filled by
non-interacting components of ideal fluids such as dark matter and holographic
dark energy. The total dark energy, which is a combination of generalized HDE
and geometric part, has a density parameter that approaches one by decreasing
the redshift. Considering the total equation of state parameter and
deceleration parameter of the universe indicates that the universe could stays
in positive accelerated expansion phase that shows an agreement with
observational data, only for the specific values of the constant $\zeta$.
