needless fear; groundless apprehension; unfounded worry
A literary or formal expression for worrying about something that is extremely unlikely to happen. Often used in the phrase 杞憂に終わる (to prove to be a groundless fear).
His worries turned out to be completely unfounded.
そんなことを心配するなんて杞憂だよ。
Worrying about something like that is just needless fear.