Article Effects of Quantum Metric Fluctuations on the Cosmological Evolution in Friedmann-Lemaitre-Robertson-Walker Geometries Zahra Haghani 1,* and Tiberiu Harko 2,3,4,5 1 School of Physics, Damghan University, Damghan 36716-41167, Iran 2 Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering (IFIN-HH), 077125 Bucharest, Romania;
[email protected] 3 Astronomical Observatory, 400487 Cluj-Napoca, Romania 4 Department of Physics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania 5 School of Physics, Sun Yat-Sen University, Guangzhou 510275, China * Correspondence:
[email protected] Abstract: In this paper, the effects of the quantum metric fluctuations on the background cosmological dynamics of the universe are considered. To describe the quantum effects, the metric is assumed to be given by the sum of a classical component and a fluctuating component of quantum origin . At the classical level, the Einstein gravitational field equations are equivalent to a modified gravity theory, containing a non-minimal coupling between matter and geometry. The gravitational dynamics is determined by the expectation value of the fluctuating quantum correction term, which can be expressed in terms of an arbitrary tensor Kmn. To fix the functional form of the fluctuation tensor, the Newtonian limit of the theory is considered, from which the generalized Poisson equation is derived. The compatibility of the Newtonian limit with the Solar System tests allows us to fix the form of Kmn. Using these observationally consistent forms of Kmn, the generalized Friedmann equations are obtained in the presence of quantum fluctuations of the metric for the case of a flat homogeneous and isotropic geometry.