To find more deliberate $f(R,T)$ cosmological solutions, we take our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most acceptable cosmological results. Our investigations are performed by applying the dynamical system approach. We obtain the cosmological parameters/quantities in terms of some defined dimensionless parameters that are used in constructing the dynamical equations of motion. The investigated parameters/quantities are the evolution of the Hubble parameter and its inverse, the “weight function”; the ratio of the matter density to the dark energy density and its time variation; the deceleration; the jerk and the snap parameters; and the equation-of-state parameter of the dark energy. We numerically examine these quantities for two general models $R+\alpha R^{-n}+\sqrt{-T}$ and $R\log {[\alpha R]}^q+\sqrt{-T}$. All considered models have some inconsistent quantities (with respect to the available observational data), except the model with $n=-0.9$, which has more consistent quantities than the other ones. By considering the ratio of the matter density to the dark energy density, we find that the coincidence problem does not refer to a unique cosmological event; rather, this coincidence also occurred in the early Universe. We also present the cosmological solutions for an interesting model $R+c_1\sqrt{-T}$ in the nonflat Friedmann–Lemaître–Robertson–Walker metric. We show that this model has an attractor solution for the late times, though with $w^{(\mathrm{DE})}=-1/2$. This model indicates that the spatial curvature density parameter gets negligible values until the present era, in which it acquires the values of the order ${10}^{-4}$ or ${10}^{-3}$. As the second part of this work, we consider the weak-field limit of $f(R,T)$ gravity models outside a spherical mass immersed in the cosmological fluid. We have found that the corresponding field equations depend on the both background values of the Ricci scalar and the background cosmological fluid density. As a result, we attain the parametrized post-Newtonian parameter for $f(R,T)$ gravity and show that this theory can admit the experimentally acceptable values of this parameter. As a sample, we present the post-Newtonian gamma parameter for general minimal power law models, in particular, the model $R+c_1\sqrt{-T}$.

• Received 7 May 2014

DOI:https://doi.org/10.1103/PhysRevD.90.044031