  We consider a model of modified gravity from the nonperturbative quantization
of a metric. We obtain the modified gravitational field equations and the
modified conservational equations. We apply it to the FLRW spacetime and find
that due to the quantum fluctuations a bounce universe can be obtained and a
decelerated expansion can also possibly be obtained in a dark energy dominated
epoch. We also discuss the effects of quantum fluctuations on inflation
parameters (such as slow-roll parameters, spectral index, and the spectrum of
the primordial curvature perturbation) and find values of parameters in the
comparing the predictions of inflation can also work to drive the current epoch
of acceleration. We obtain the constraints on the parameter of the theory from
the observation of the big bang nucleosynthesis.
