In Zoroastrianism
Varuna is not attested in the texts of the Avesta. The closest sea deity in Zoroastrian cosmology is Vourukasha; and the nearest homonym is Varena, the four-cornered fourteenth region of the world (Vendidad 1.17) and populated by "fiends" and "savage, non-Aryan natives" (Vd 7.10). In Yasht 15, Haoshyangha begs for a boon that he might smite "two-thirds of the daevas of Mazana and of the fiends of Varena". (Yt 15.2.6) An individual who does not follow daena " religion" is an anya-varena. (Yasna 16.2; Vd 12.21, 15.2)
Too late to be of relevance to a reconstruction of what might have happened to Indo-Iranian *vouruna (if at all such a predecessor figure existed) in Iran is the "Varuna" of the circa 9th century texts of Zoroastrian tradition (the so-called "Pahlavi" texts), and in the early New Persian Shahnameh. In both cases this Varuna is a dim-witted, easily tricked demon of "backwards"-ness, which is the literal Middle Persian meaning of his name.
Assuming that Vedic Varuna is not a purely Indian development (i.e. assuming that he derives from an Indo-Iranian *vouruna), there are several different theories on what might have happened to Indo-Iranian *vouruna in Iran:
Nyberg (Die Religionen des alten Iran, 1938:282ff) sees Varuna represented as the Amesha Spenta Asha Vahishta "Best Righteousness", an opinion—with extensions—that Dumezil (Tarpeia 1947:33-113) and Widengren (Die Religionen Irans, 1965:12-13) also follow. This theory is based on Vedic Varuna's role as the principal protector of rta, which in Iran is represented by asha .
Kuiper (IIJ I, 1957) proposes that none less than Ahura Mazda is a development from an earlier dvandva *vouruna-mitra. The basis of Kuiper's proposal is that the equivalent of Avestan mazda "wisdom" is Vedic medhira, described in Rigveda 8.6.10 as the "(revealed) insight into the cosmic order" that Varuna grants his devotees. In Kuiper's view, Ahura Mazda is then a compound divinity in which the propitious characteristics of *mitra negate the unfavorable qualities of *vouruna.
Zimmer (Münchner Studien 1984:187-215) observed that Varuna has the byname (cult epithet) bhaga, an adjective that also appears in the Avesta (as baga). It may then be that the Avestan adjective is likewise a cult epithet, the proper name having been forgotten—a not uncommon occurrence. This may be seen to be reflected in Artaxerxes III's invocation of ahuramazda ura mithra baga "Ahura Mazda, Mithra, and the Baga" (Boyce, Acta Iranica 21, 1981:59-73).
Another epithet of Vedic Varuna is asura, and there may be a remnant of Varuna in those Gathic passages (generally presumed to have been composed by Zoroaster himself) refers to the ahuras (plural) without (aside from Ahura Mazda) explicitly naming them. While Ahura Mazda is uniformly "the mightiest Ahura" (e.g. Yasna 33.11), in the only two occurrences of the term where the word does not refer to Ahura Mazda, the poet uses the expression mazdasca ahurano (Yasna 30.9, 31.4). This phrase, generally understood to mean "the Wise One and the (other) Ahuras", is in "common opinion" (so Boyce 1984:159) recognized as being archaic and in which the other Ahuras are *mitra and *varouna. Boyce (Mithra the King and Varuna the Master, 2001) sees this supported by the younger Avestan dvandvah expression mithra ahura berezanta "Mithra and the High Lord", the latter being unambiguously Ahura Berezainti, "High Lord" Apam Napat, the third member of the Ahuric triad (Gray, Foundations, 1929:15), and with whose Indian equivalent (also Apam Napat) Vedic Varuna is closely associated.
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