Holographic entropy bound and a special class of spherical systems in cosmology

The holographic entropy bound is discussed in cosmology. Inspired by the work of Fischler and Susskind [hep-th/9806039], we aim to define a special class of spherical systems in cosmology, within which the entropy of matter remains compliant with the holographic entropy bound throughout the evolution of the universe, irrespective of the universe's components. It is found that if the entropy of matter per unit co-moving volume is bounded from above, such a special class of spherical systems indeed exists. Moreover, the matter contained within a unit co-moving volume can be replaced by a black hole of the same mass-energy. Provided that the entropy of the black hole consistently exceeds that of the matter it replaces, there is also a unified definition for these special spherical systems.