Scholars at the Great Library of Alexandria unanimously deemed Aeschylus to be the author of Prometheus Bound. Since the 19th century, however, several scholars have doubted Aeschylus' authorship of the drama. These doubts initially took the form of the "Zeus Problem." That is, how could the playwright who demonstrated such piety toward Zeus in The Suppliants and Agamemnon be the same playwright who inveighs against Zeus for being a violent tyrant? This objection prompted the theory of a Zeus who (like the Furies in the Oresteia) "evolves" in the course of the trilogy. Thus, by the conclusion of Prometheus the Fire-Bringer, Aeschylus' Zeus would be more like the just Zeus found in the works of Hesiod.
Arguments for and against the attribution to Aeschylus have been based on metrical-stylistic grounds: the play's diction, the use of so-called Eigenworter, the use of recitative anapests in the meter, etc. In 1977, Mark Griffith made a case against the attribution. C. J. Herington, however, repeatedly argued for it. Since Griffith's landmark study, confidence in Aeschylean authorship has steadily eroded. Influential scholars such as M.L West, Alan Sommerstein, and Anthony Podlecki have made arguments against authenticity. West has argued that the Prometheus Bound and its trilogy are at least partially and probably wholly the work of Aeschylus' son, Euphorion, who was also a playwright. Based upon allusions to Prometheus Bound found in the works of comic playwright Aristophanes, Podlecki has recently suggested that the tragedy might date from ca. 415 BC. Those who trust in the verdict of antiquity and still favor Aeschylean authorship have dated the play anywhere from the 480s to 456 BC.