  We study the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology in the
Weyl-transverse (WTDiff) gravity in a general space-time dimension. The WTDiff
gravity is invariant under both the local Weyl (conformal) transformation and
the volume preserving diffeormorphisms (transverse diffeomorphisms) and is
believed to be equivalent to general relativity at least at the classical level
(perhaps, even in the quantum regime). It is explicitly shown by solving the
equations of motion that the FLRW metric is a classical solution in the WTDiff
gravity only when the spatial metric is flat, that is, the Euclidean space, and
the lapse function is a nontrivial function of the scale factor.
