You can't go around making these unsubstantiated allegations without any proof to back them up.你不能在没有任何佐证的情况下到处传播这些未经证实的说法。

unsubstantiated rumours about his private life有关他私生活的捕风捉影的谣言

I do object to their claim, which I find totally unsubstantiated.我的确反对他们的说法, 在我看来那是毫无根据的。