Tae Hun Kim, «The Anarthrous ui(o\j qeou= in Mark 15,39 and the Roman Imperial Cult», Vol. 79 (1998) 221-241
This article points up evidence by which the language of the Roman imperial cult might help make clearer what a reader of Mark's Gospel might understand when the centurion (Mark 15,39) refers to Jesus as ui(o\j qeou=. Knowing how an audience familiar with this cult language would react, Mark intentionally speaks of Jesus as ui(o\j qeou= at 1,1, as well as at 15,39.
used the name divi filius (or qeou= ui(o\j) and this seems to support the view that divi filius (or qeou= ui(o\j) was not a title that could be applied to Roman emperors in general.
Gaius Caligula (37-41 CE): ne/wi qew=i (IGR IV 1094) = "new god"; 1Arhoj ui(o/n (CIA III 444a) = "son of Ares"; Sebastou= ui(o\n ne/on 1Arh (CIA III 444) = "son of Augustus, a new Ares" 35.
Claudius (41-54 CE): Tibe/rioj Klau/dioj ku/rioj (SB 4331) = "Tiberius Claudius lord"; Tibe/rioj Klau/dioj Kai=sar Sebasto\j au)tokra/twr o( ku/rioj (GOA 1038) = "Emperor Tiberius Claudius Caesar Augustus, the lord"; qeo\j Klau/dioj (PSI 1235; POxy 713) = "Claudius god"; qeo\j Kai=roj (POxy 808; POxy 1021) = "Caesar god"; qeo\j Sebasto/j (PMich 244) = "Augustus god"; o( ku/rioj (OPetr 209) = "The lord."
Nero (54-58 CE): Ne/rwn o( ku/rioj (PLond 1215; POxy 246; GOA 1038) = "Nero the lord"; Ne/rwn Kai=sar o( ku/rioj (OPetr 288; POxy 246) = "Nero Caesar the lord"; Ne/rwn Klau/dioj Kai=sar... o( swth\r kai\ eu)erge/thj th=j oi(koume/nhj (OGIS 668) = "Nero Claudius Caesar the savior and benefactor of the inhabited world"; )Agaqo\j Dai/mwn th=j oi)koume/nhj a)rxh\ w1n te pa/ntwn a)gaqw=n (POxy 1021) = "The good god of the inhabited world, the beginning of all good things"; to\n uio\n tou= megi/stou qew=n (IM 157b) = "the son of the greatest of the gods"; o( tou= panto\j ko/smou ku/rioj Ne/rwn (SIG 814) = "Nero Lord of the whole world."
Vespasian (69-79 CE): Ou)espasiano\j o( ku/rioj (POxy 1439; SB 1927) = "Vespasian the lord"; Ou)espasiano\j au)tokra/twr o( ku/rioj (GOA 439; SC 3563) = "Emperor Vespasian, the lord"; qeo\j Ou)espasiano\j (POxy 257; POxy 1112) = "Vespasian god".
Considering the philological and archaeological evidence presented, therefore, it seems plausible that the name divi filius (or qeou= u(io\j was unique to Augustus and was probably not used by any other emperor beside himself 36. Johnson has argued that