My question may seem bizarre, since in our age marriage is a juridical institution widely regulated in every nation, with the presence of witnesses and a precise registration in public registers; however I am interested in the exquisitely halachic aspect.
My doubts arise from the following passages of Rambam’s Mishneh Torah:
Hilchot Ishut 1:1
Before the Torah was given, when a man would meet a woman in the marketplace and he and she decided to marry, he would bring her home, conduct relations in private and thus make her his wife. Once the Torah was given, the Jews were commanded that when a man desires to marry a woman, he must acquire her as a wife in the presence of witnesses. [Only] after this, does she become his wife. This is [alluded to in Deuteronomy 22:13]: "When a man takes a wife and has relations with her...."
Hilchot Melachim 9:8
When is a Gentile woman considered divorced? When her husband removes her from his home and sends her on her own or when she leaves his domain and goes her own way. They have no written divorce proceedings.
From what Rambam says it would seem that, from a halachic point of view, the requirement for marriage between Gentiles is simple cohabitation, and that Halakhah considers the presence of a written legal act irrelevant to the Gentiles to ascertain the constitution and / or the dissolution of the marriage bond (I do not understand however, at this point, how were legally distinguished the wives and the pilagshim mentioned in the Pentateuch before Matan Torah: perhaps the pilagshim were all slaves, as about some pilagshim it is explicitly said in the book of Genesis?)
The issue has considerable relevance, as among the Noahide Laws there is a ban on sexual intercourse with a married woman (adultery), and therefore it is essential to know when a Gentile woman is to be considered married or not on the halachic level. According to what Rambam says, even the cohabitation between Gentiles so-called "more uxorio", that is, without the celebration of a marriage according to the state's binding laws, would still qualify as a marriage for the Halakhah, but perhaps I misunderstood.