Baseless, groundless, unfounded, unwarranted mean not justified or justifiable in any way.
Baseless implies an entire lack of foundation; it imputes to a thing lack of actuality in itself or in the events or facts upon which it is supposedly based.
Groundless stresses the absence of a cause or reason; it is applied especially to thoughts, emotions, or feelings that arise seemingly from nothing and have no perceptible or justifying cause.
Unfounded sometimes implies baselessness but more often suggests lack of support or want of evidence, authority, or proof.
Unwarranted emphasizes the fact of exceeding the bounds of what is authorized, sanctioned, believable, or reasonable.