We do not currently know of any synonyms for pornocracy.
The proper noun pornocracy is defined as:
The period of the papacy known as the saeculum obscurum (Latin for “dark age”), and also as the “Rule of the Harlots”, which began with the installation of Pope Sergius III in 904 and lasted for sixty years until the death of Pope John XII in 964, during which time the popes were strongly influenced by the Theophylacti, a powerful and corrupt aristocraticfamily. [from mid-19th c.]