  The covariant entropy bound conjecture is an important hint for the quantum
gravity, with several versions available in the literature. For cosmology,
Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity
theory and one version of this conjecture. Recently, S. He and H. Zhang
proposed a version for the dynamical horizon of the universe, which validates
the entropy bound conjecture for the cosmology filled with perfect fluid in the
classical scenario when the universe is far away from the big bang singularity.
However, their conjecture breaks down near big bang region. We examine this
conjecture in the context of the loop quantum cosmology. With the example of
photon gas, this conjecture is protected by the quantum geometry effects as
expected.
