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Although it was proved that the Nash theory doesn't have classical Einsteinlimits, it has been proven to be formally divergent free and considered to beof interest in constructing theories of quantum gravity. The original Nashgravity without matter contents can't explain the current accelerated expansionof the Universe. A possible extension of theory is by adding some mattercontents to the model. In this work, we generalize the Nash theory of gravityby adding the matter fields. In order to examine the effects of thisgeneralization, we first derive the equations of motion in the flat FLRWspacetime and examine the behaviors of the solutions by invoking specific formsof the Hubble parameter. We also classify the physical behaviors of thesolutions by employing the stability analysis and check the consistency of themodel by considering particular cosmological parameters.

On Nash theory of gravity with matter contents