The golden bough is a reference to a mystical tree in a Greco-Roman myth. In the ancient tale the hero Aeneas consults the prophetess who is one of the Sybil at Cumae. The Sybil tell Aeneas to break a branch from a certain tree that is sacred to Juno Inferno (Proserpina). Then Aeneas is led to the entrance of the Underworld that he descends. Aeneas approaches the Stygian lake that Charon will not ferry him across because he is not dead. The Sybil who accompanies Aeneas then produces a Golden Bough that allows Aeneas entrance into the Underworld.
This tale is similar to the one of the Celtic hero Bran who is guided by a fairy woman, bearing the Silver Branch, through which he gains admittance to the Fairy Realm. The Golden Bough, like the Silver Branch, is a passport to another realm.
In James Frazer’s book The Golden Bough he deals with the cult of Diana and the Dianus at Lake Nemi, the sanctuary of the goddess Diana. In this version, Frazer includes in the tale of Aeneas many similarities to the lore of Lake Nemi and the mysterious figure of Rex Nemorensis, the King of the Woods. Frazer was especially struck by the fact that the branch had to be broken from the sacred tree at Nemi in order to gain entrance to the sacred grove to challenge the guardian. This, to Frazer, was not unlike Aeneas confronting Charon.
Within the mystical tree symbolism, the folk in the branch represents the division of good and evil, light and dark. In the initiatory rites of Prosepina the branch was held up to her as an offering. Such an offering symbolized that the bearer understood her polarity, and that to enter the darkness was to return to the light. Only by possessing such knowledge would Prosepina embrace anyone entering her realm. Also this symbolizes the spiral dance that embraces the identical theme. A.G.H.
Source: 78, 157-158.