Narrow Results

This paper explores cosmic evolution in $f(R,T)$ gravity considering two distinct models with minimal coupling that are linear and quadratic in $T$; $f(R,T)=R+\alpha T$ and $f(R,T)=R+\alpha T^2$. The flat FRW space-time under the matter and radiation distribution has been considered to complete the analysis. In this background, the dynamical equations for dust in terms of dimensionless variables are developed. Via solutions of these dynamical equations, we develop significant cosmological parameters to compare the obtained results with the $\mathrm{\Lambda }$CDM model and analyze them graphically. It is found that these parameters efficiently explain the expanding phenomenon of the universe for constrained values of the involved model parameters using some recent observational data. Moreover, the results are found to be stable via the square speed of sound. The matter and radiation fixed points are calculated by an autonomous set of dynamical equations, which are the stable and unstable saddle points. Also, the growth of matter perturbation in the $f(R,T)$ theory has been discussed. Under this scenario, it is also checked that exact solutions of the dynamical equations are not possible for non-minimal coupling between geometry and matter.

A modified $f(R)$ viable model is proposed that behaves asymptotically as $\mathrm{\Lambda }$CDM and satisfies cosmological and local gravity constraints. Apart from a mass scale that is a priori defined, the model contains only one additional parameter, which is determined by the current value of the matter density parameter ${\mathrm{\Omega }}_{m0}$. Under the chameleon mechanism the model satisfies the thin shell restrictions for local gravity systems without imposing additional restrictions on model parameters. Signals of scalar–tensor regime in the growth of matter perturbations, are present. Using the mass scale to determine the matter density parameter today, the remaining free parameter covers the whole range of values needed to test the model against the more stringent constraints arising at galactic and galactic cluster scales. The finite time singularity of the model was analyzed. A comparison was made with known models with the same number of parameters.