  The de Sitter (dS) entropy bound gives the maximal number of e-folds that
non-eternal inflation can last before violating the thermodynamical
interpretation of dS space. This semiclassical argument is the analogue, for dS
space, of the Black-Hole information paradox. We use techniques developed to
address the latter, namely the island formula, to calculate semiclassically the
fine-grained entropy as seen by a Minkowskian observer after inflation and find
that this follows a Page-like curve, never exceeding the thermodynamic dS
entropy. This calculation, performed for a CFT in 2D gravity, suggests that the
semiclassical expectation should be modified in such a way that the entropy
bound might actually not be present.
