  Friedmann-Lemaitre-Robertson-Walker (FLRW) model, representing the isotropic
and homogeneous Universe, has an inherent diffeomorphism (or reparametrization)
invariance. For a given local time-reparametrization symmetry transformation of
(0+1)-dimensional (1D) diffeomorphism invariant FLRW model, we derive the
off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry
transformations in a consistent manner. The supervariable approach to BRST
formalism is used as a guiding tool in finding the proper (anti-)BRST
transformations. An application of (super-)diffeomorphism invariance, in the
context of superspace formalism, yields horizontality conditions. Moreover, the
celebrated CF-type condition which is universal for 1D diffeomorphism invariant
theories, emerges as an off-shoot of the horizontality condition and provides
the absolute anticommutativity of the (anti-)BRST transformations. In addition,
this CF-type condition leads to the derivation of coupled (but equivalent)
(anti-)BRST invariant quantum Lagrangians for FLRW model. We also capture the
geometrical interpretation of the (anti-)BRST transformations and their
properties in terms of the Grassmannian translational generators and
supervariables.
