  Bousso's entropy bound is a conjecture that the entropy through a null
hypersurface emanating from a two-dimensional surface with a nonpositive
expansion is bounded by the area of that two-dimensional surface. We
investigate the validity of Bousso's entropy bound in the spatially flat,
homogeneous, and isotropic universe with an adiabatic entropy current. We find
that the bound is satisfied in the entire spacetime in which a cutoff time is
introduced based on the entropy density and the energy density. Compared to the
previously used prescription which puts a cutoff near the curvature
singularity, our criterion for introducing the cutoff is applicable even to a
nonsingular universe. Our analysis provides an interpretation of the
incompleteness implied by the recently proposed singularity theorem based on
the entropy bounds.
