Invictus as epithet
Invictus ("unconquered, invincible") was an epithet utilized for several Roman deities, including Jupiter, Mars, Hercules, Apollo, and Silvanus. It had been in use from the 3rd century BC. The Roman cult to Sol is continuous from the "earliest history" of the city until the institution of the Christian cult as the exclusive state religion. Scholars have sometimes regarded the traditional Sol and Sol Invictus as two separate deities, but the rejection of this view by S. E. Hijmans has found supporters.
An inscription of AD 102 records a restoration of a portico of Sol in what is now the Trastevere area of Rome by a certain Gaius Iulius Anicetus. While he may perhaps have had in mind an allusion to his own cognomen, which is the Latinized form of the Greek equivalent of invictus, ἀνίκητος (aniketos), the earliest extant dated inscription that uses invictus as an epithet of Sol is from AD 158. Another, stylistically dated to the 2nd century, is inscribed on a Roman phalera (ornamental disk): inventori lucis soli invicto augusto ("to the contriver of light, sol invictus augustus"). Augustus is a regular epithet linking deities to the Imperial cult.
Sol Invictus played a prominent role in the Mithraic mysteries, and was equated with Mithras. The relation of the Mithraic Sol Invictus to the public cult of the deity with the same name is unclear and perhaps non-existent.