Is the universal dominion of the prophets and messengers, such as the power of Solomon, peace be upon him, to subjugate the wind and jinn, restricted to their lives, or does it continue after their death?

The phrase "cosmic authorities" is not a recognized term. What Allah supported His messengers with is called "miracles." A miracle is an extraordinary event that Allah makes apparent through a prophet to challenge his people, and it is called such because humans are incapable of producing anything like it. The word "miracle" (mu'jiza) is not found in the Quran; rather, the word "sign" (ayah) is used. Allah supported all prophets with miracles, some of which ceased when their purpose was fulfilled, like the miracles of Solomon, and some of which remain. Among Solomon's miracles was the fulfillment of his supplication: "He said, 'My Lord, forgive me and grant me a kingdom such as will not belong to anyone after me. Indeed, You are the Bestower.'" As for this continuing after his death, it has no meaning.