  We introduce the cosmic holographic bounds with two UV and IR cutoff scales,
to deal with both the inflationary universe in the past and dark energy in the
future. To describe quantum fluctuations of inflation on sub-horizon scales, we
use the Bekenstein-Hawking energy bound. However, it is not justified that the
D-bound is satisfied with the coarse-grained entropy. The Hubble bounds are
introduced for classical fluctuations of inflation on super-horizon scales. It
turns out that the Hubble entropy bound is satisfied with the entanglement
entropy and the Hubble temperature bound leads to a condition for the slow-roll
inflation. In order to describe the dark energy, we introduce the holographic
energy density which is the one saturating the Bekenstein-Hawking energy bound
for a weakly gravitating system. Here the UV (IR) cutoff is given by the Planck
scale (future event horizon), respectively. As a result, we find the close
connection between quantum and classical fluctuations of inflation, and dark
energy.
