  One of the standard approaches of incorporating the quantum gravity (QG)
effects into the semiclassical analysis is to adopt the notion of a
quantum-corrected spacetime arising from the QG model. This procedure assumes
that the expectation value of the metric variable effectively captures the
relevant QG subtleties in the semiclassical regime. We investigate the
viability of this effective geometry approach for the case of dust dominated
and a dark energy dominated universe. We write the phase space expressions for
the geometric observables and construct corresponding Hermitian operators. A
general class of operator ordering of these observables is considered, and
their expectation values are calculated for a unitarily evolving wave packet.
In the case of dust dominated universe, the expectation value of the Hubble
parameter matches the "semiclassical" expression, the expression computed from
the scale factor expectation value. In the case of Ricci scalar, the relative
difference between the semiclassical expression and quantum expectation is
maximum at singularity and decays for late time. For a cosmological constant
driven universe, the difference between the semiclassical expressions and the
expectation value is most pronounced far away from the bounce point, hinting at
the persistent quantum effect at the late time. The parameter related to the
shape of the distribution appears as a control parameter in these models. In
the limit of a sharply peaked distribution, the expectation value of the
observables matches with their semiclassical counterpart, and the usage of
effective geometry approach is justified.
