The Roman Empire was not divided and Christianity developed
under a unified empire.
Mainstream Christianity was composed of Latin or Western
Christianity and Greek or Eastern Christianity. The former was the
main form of Christianity in the western part of the Roman Empire
and the latter was the main form of Christianity in the eastern
part of the Roman Empire. Later they came to be called Catholic and
Orthodox respectively. At that time they considered themselves to
be two branches of one church, which they called Catholic. Both
churches subscribed to the Nicene Creed, which upheld
Trinitarianism; that is, the concept of the Holy Trinity. This
creed was issued at the first ecumenical council held in Nicaea in
325.
There were also dissident Christian doctrines such as Arianism,
Monophysitism, Miaphysitism, Psilanthropism, Modalism (or
Sabellianism), Marcionism, Docetism and Gnostic Chisitanity. These
doctrines begged to differ with the Nicene Creed in matters of
Christology (the theology of the nature of the person of Jesus) and
were non-Trinitarian. There was also Novatism and Donatism, which
had a more rigorist theology that that of the Nicene Creed.
The most important dissident Christian doctrine was Arian
Christianity (named after Arius, a presbyter form Alexandria) which
was popular around the Roman Empire and was also adopted by the
peoples who invaded the western part of the Roman Empire (Vandals,
Sueves, Aland and Burgundians) and by the Goths (both the Visigoths
and the Ostrogoths).
In 380 the co-emperors Theodosius I (or the Great) and Gratian
issued Edict of Thessalonica. This made mainstream Christianity
(the Nicene Creed) the sole legitimate religion of the Roman
Empire. The purpose of the edict was to ban dissident Christian
doctrines, which were branded as heretic. Theodosius started to
persecute them soon afterwards. His main target was Arian
Christianity. He also expelled Demophilus of Constantinople, the
most important Arian Bishop.