Abstract
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a nonminimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the nonminimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.
Highlights
Modified gravity theories may provide an attractive alternative to the standard explanations of the present day observations that have shaken the well-established foundations of theoretical physics
The necessity of explaining the late time acceleration lead to the formulation of a new paradigm in theoretical physics and cosmology, which postulates that the explanation of the late time acceleration is the existence of a mysterious component of the Universe, called dark energy (DE), which can describe the late time dynamics of the Universe [6,7], and can explain all the observed features of the recent cosmological evolution
In the present section we will briefly review the fluctuating metric approach to quantum gravity, we will discuss its relation with standard semi-classical gravity, and we will point out the quantum mechanical origins of the modified gravity models with geometry–matter coupling
Summary
Modified gravity theories may provide an attractive alternative to the standard explanations of the present day observations that have shaken the well-established foundations of theoretical physics. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation. From a physical point of view a non-zero divergence of the energymomentum tensor can be interpreted as corresponding to an irreversible energy flow from the gravitational field to the matter fluid Such an irreversible thermodynamic process is the direct consequence of the non-minimal curvature-matter coupling, induced in the present case by the quantum fluctuations of the metric [25,44,45].
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