Dynamical aspects of the energy–momentum squared gravity in the scalar tensor representation

In this paper we have revisited the energy–momentum squared gravity theory, by taking into account the second derivative of the matter Lagrangian with respect to the metric, encapsulating relations originated from thermodynamical grounds. The study has focused on the inclusion of new specific relations related to the second derivative of the matter Lagrangian with respect to the metric, giving rise to a different final form for the evolution equations in the scalar tensor representation. In the previous studies this term has been neglected, since it was associated to a possible divergence in the scenario where the matter component behaves like a non-relativistic collisionless fluid. After obtaining the scalar tensor representation of the energy–momentum squared gravity with the new corrections, we have analyzed the physical implications by relying on the linear stability theory. The results show that the current cosmological system is compatible with the expansion of the Universe for some specific matter Lagrangians, explaining the emergence of matter domination era, approaching the late time accelerated expansion era close to the de-Sitter phenomenology. In this case we have obtained possible analytical constraints for specific model’s parameters from the viewpoint of dynamical analysis.