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

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology