The Greek word aigis represented the shield worn by Zeus, a shield he later on gave Athena to show his protection of her. This shield was made of goat skin, and truly the Proto Indo European roof to this word, aig, represented ‘a goat’. In later times, aegis represented a large collar or cape worn by a person to signify the protection provided to him by a high religious authority. In modern times this great noun represents sponsorship, economic protection.
Why this word?
This word maps the history of power relations through its varying meaning. In ancient Greece, when power was attested to human Gods, wearing something given to you by a God was enough to protect you. In later times, as worldly power was attested to religious (mainly Christian) emissaries, wearing a certain cape provided to you by the church- was enough for one to be almighty. Nowadays, protection is money; thus the sense of sponsorship.
I see absolutely no reason not to use aegis to represent any sort of protection, not only the sort visible today.
How to use aegis?
Aegis is a noun, mostly used with a complement; saying “I have aegis” would be weird, but “I have the aegis of…” is absolutely fine.
Mother: “Are you sure you absolutely have to go there? I really don’t like that neighborhood”. Dana: “That’s really okay mom, David is going with me; I have his aegis”.
In the more monetary sense, you would use this word with ‘under the’, for example: “the arts and education programs of the United Nations are under the aegis of UNESCO”.