Effects of quantum fluctuations of metric on the universe

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.