Other forms: groundlessly
Something that's groundless isn't valid or justified, like your groundless fear that you failed your math quiz, even though you studied and knew all the material.
Grounds are "factors forming the justification for a belief," and when you don't have any such grounds, your belief is groundless. In other words, anything groundless has no reason or cause to back it up. A groundless claim is one that has no proof, and a groundless suspicion is empty: "We questioned that nice lady next door and made her cry, thanks to your groundless accusation that she stole our cat."