  Although it was proved that the Nash theory doesn't 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 can't explain the current accelerated expansion
of the Universe. A possible extension of theory is by adding some matter
contents to the model. In this work, we generalize the 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
spacetime 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.
