Observational limits on the Nash theory of gravity with matter contents

We generalize the original Nash theory of gravity by adding the matter fields by specifying a proper form of the field equations on more general footings for space with matter contents. We first derive the equations of motion in the flat Friedmann-Lemaitre-Robertson-Walker (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. We check the consistency of the model by considering particular cosmological parameters. We use observational data from Supernovae Ia (SNeIa) and baryonic acoustic oscillations (BAO) to constrain the parameters of the model. Interestingly, we discover the best fit of our model with ωm0 = 0.25 and H0 = 0.4 for τ0 = 0.3 and ρ0 = 0.5 assuming the Hubble parameter H ρ-2.