Bousso's Covariant Entropy Bound and Padmanabhan's Emergent Universe
  We study the Padmanabhan's emergent Universe in the context of Bousso's covariant entropy conjecture. We find that for a flat Universe, this conjecture can be applied for the system of Padmanabhan's emergent Universe. It turns out that the maximum "bulk entropy" of Padmanabhan's emergent Universe coincides with the upper bound of Bousso's covariant entropy on the null surface defined by Hubble horizon, provided that the Universe is just filled by the cosmological constant or radiation field which represent maximal entropy during inflation and subsequent radiation dominant era. This maximal entropy is lost by the appearance of matter system in the Universe at matter dominant era. Applying D-bound on the matter system in the Padmanabhan's emergent Universe, we find that the apparent cosmological horizon of a flat Universe in matter dominant era has less area and entropy than those (maximal) of apparent cosmological horizon of an empty de-Sitter space, in complete agreement with our conclusion. The maximal area and entropy in the Padmanabhan's emergent Universe are recovered "as soon as possible" by transition from matter dominant to cosmological constant eras, provided that the matter inside the Universe is moved completely outward the apparent cosmological horizon in "an accelerating way" at late times. 
H. Hadi, Y. Heydarzade and F. Darabi
gr-qc