authority vs imperium

authority and imperium both are nouns.

Word	Noun	Adjective	Verb	Adverb
authority	Yes	No	No	No
imperium	Yes	No	No	No

As nouns, imperium is a hyponym of authority; that is, imperium is a word with a more specific, narrower meaning than authority:

Other hyponyms of authority include power of appointment, carte blanche, command, lordship, muscle, sovereignty.

authority (noun)	imperium (noun)
the power or right to give orders or make decisions	supreme authority; absolute dominion
official permission or approval	the domain ruled by an emperor or empress; the region over which imperial dominion is exercised
freedom from doubt; belief in yourself and your abilities
an authoritative written work
an administrative unit of government
an expert whose views are taken as definitive
(usually plural) persons who exercise (administrative) control over others