In this paper we undertake the modified theory of gravity f (R, T ), where R and T are the Ricci scalar and the trace of the energy momentum tensor, respectively. Imposing the conservation of the energy momentum tensor, we obtain a model about what dynamics and stability are studied. The stability is developed using the de Sitter and power-law solutions. The results show that the model presents stability for both the de Sitter and power-law solutions. Regarding the dynamics, cosmological solutions are obtained by integrating the background equations for both the low-redshift and High-redshift regimes and are consistent with the observational data.

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In this paper, we investigate the late-time cosmic acceleration in mimetic f (R, T ) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from Q(z) and the well-known particular model f (R, T ), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f (R, T ) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f (R, T ) gravity can be damped.

This paper is devoted to the reproduction of the gravitational baryogenesis epoch in the context of f (R, T ) theory of gravity, where R and T are respectively the curvature scalar and the trace of the energy-momentum tensor, respectively. It is assumed a minimal coupling between matter and gravity. In particular we consider the following two models, f (R, T ) = R + αT + βT 2 and f (R, T ) = R + µR 2 + λT , with the assumption that the universe is filled by dark energy and perfect fluid where the baryon to entropy ratio during a radiation domination era is non-zero. We constrain the models with the cosmological gravitational baryogenesis scenario, highlighting the appropriate values of model's parameters compatible with the observation data of the baryon-entropy ratio.