  We analyze the validity of the generalized covariant entropy bound near the
apparent horizon of isotropic expanding cosmological models. We encounter
violations of the bound for cosmic times smaller than a threshold. By
introducing an infrared cutoff we are able to mantain the bound for a radiation
dominated universe. We study different physical mechanisms to restore the
bound, as a non-additivity of the entropy at a fundamental level and/or a
cosmological uncertainty relation.
