In the context of Greek mythology, the "golden apple" refers to the story of the Judgment of Paris, which is a pivotal event leading to the Trojan War. The golden apple was inscribed "to the fairest" and was thrown by Eris, the goddess of discord, among the goddesses Hera, Athena, and Aphrodite. Paris, a Trojan prince, was chosen to decide who would receive the apple.
While this myth does not directly involve Sparta, it does touch on the themes