On Nash theory of gravity with matter contents

One of the alternative theories to Einstein's general theory, a divergence-free theory was proposed by J. Nash with Lagrangian density given by 2RμνRμν - R2. Although it was proved that the Nash theory does not have classical Einstein limits, it has been proven to be formally divergent free and considered to be of interest in constructing theories of quantum gravity. The original Nash gravity without matter contents cannot explain the current acceleration expansion of the Universe. A possible extension of theory is by adding some matter contents to the model. In this work, we generalize Nash theory of gravity by adding the matter fields. In order to examine the effects of this generalization, we first derive the equations of motion in the flat FLRW space-time and examine the behaviors of the solutions by invoking specific forms of the Hubble parameter. We also classify the physical behaviors of the solutions by employing the stability analysis and check the consistency of the model by considering particular cosmological parameters.