without rational basis: groundless fears.

before 900; Middle English: bottomless, unfathomable; Old English grundlēas. See ground1, -less

groundlessly, adverb
groundlessness, noun

baseless, unfounded, unjustified, idle. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
Cite This Source Link To groundless
World English Dictionary
groundless (ˈɡraʊndlɪs)
without reason or justification: his suspicions were groundless

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Example sentences
More than a decade later, their fears appear to have been groundless.
If what she says is true, her claim is not groundless.
Their concerns, it would seem, are not entirely groundless.
We don't even know what g is, or if it exists, so the idea that it can be
  measured is evidentially groundless.
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