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In general, one can propose a modified gravity by replacing the Einstein-Hilbert Lagrangian with different functions of the Ricci scalar, known as ƒ ( R ) theory. We consider a model of modified gravity from the nonperturbative quantization of a metric, namely decomposing the metric operator into a sum of a classical metric and a fluctuating part. We obtain the modified gravitational field equations and the modified conservational equations. We apply it to the Friedmann-Lemaitre-Robertson-Walker spacetime, obtain the modified Friedmann equations. We find that due to the quantum fluctuations a bounce universe can be obtained and a decelerated expansion can also possibly be obtained even in a dark energy dominated epoch, we also constrain the related parameters according to the physical conditions. We not only analyze the effects of quantum fluctuations on the evolutions of the radiation and dust, but also present the its modifications on inflation parameters, such as slow-roll parameters, spectral index, and the spectrum of the primordial curvature perturbation.

Effects of quantum fluctuations of metric on the universe